a non hyponormal operator generating stieltjes moment sequences abstract a linear operator s in a complex hilbert space h for which the set d s of its c vectors is dense in h and s n f 2 n 0 is a stieltjes moment sequence for every f d s is said to generate stieltjes moment sequences it is shown that there exists a closed non hyponormal operator s which generates stieltjes moment sequences what is more d s is a core of any power s n of s this is established with the help of a weighted shift on a directed tree with one branching vertex the main tool in the construction comes from the theory of indeterminate stieltjes moment sequences as a consequence it is shown that there exists a non hyponormal composition operator in an l 2 space over a finite measure space which is injective paranormal and which generates stieltjes moment sequences the independence assertion of barry simon s theorem which parameterizes von neumann extensions of a closed real symmetric operator with deficiency indices 1 1 is shown to be false

hamburger and stieltjes moment problems in several variables in this paper we give solutions to the hamburger and stieltjes moment problems in several variables in algebraic terms via extended sequences some characterizations of the uniqueness of the solutions are also presented

unbounded subnormal weighted shifts on directed trees ii abstract a new method of verifying the subnormality of unbounded hilbert space operators based on an approximation technique is proposed diverse sufficient conditions for subnormality of unbounded weighted shifts on directed trees are established an approach to this issue via consistent systems of probability measures is invented the role played by determinate stieltjes moment sequences is elucidated lambert s characterization of subnormality of bounded operators is shown to be valid for unbounded weighted shifts on directed trees that have sufficiently many quasi analytic vectors which is a new phenomenon in this area

on the moment determinance and random mixture of nakagami m variates we study complex valued nakagami m variates establishing the moment determinance of the envelope phase and joint envelope phase nakagami m probability density functions pdf s inspired by that result we then show that nakagami m variates with arbitrary fading figure m can be accurately decomposed onto a mixture of nakagami m variates with integer or half integer m i e 2m the latter has the immediate theoretical implication that results currently known to hold for nakagami m channels under the constraint 2m can accurately be extended to arbitrary m via simple linear decomposition with weights given by the random mixture probabilities for which formulas are provided the latter is illustrated with an example of the application of the random mixture decomposition to the simplification and generalization of bit error rate ber expressions for psk modulation in the nakagami m relay channel for completeness implications on possible extensions and improvements of existing methods to generate nakagami m variates is also briefly discussed in the form of further examples

the truncated complex moment problem let 2n denote a sequence of complex numbers 00 01 10 0 2n 2n 0 00 0 ij ji and let k denote a closed subset of the complex plane c the truncated complex k moment problem for entails determining whether there exists a positive borel measure on c such that ij zizj d 0 i j 2n and supp k for k kp a semi algebraic set determined by a collection of complex polynomials p pi z z mi 1 we characterize the existence of a finitely atomic representing measure with the fewest possible atoms in terms of positivity and extension properties of the moment matrix m n and the localizing matrices mpi we prove that there exists a rankm n atomic representing measure for 2n supported in kp if and only if m n 0 and there is some rankpreserving extension m n 1 for which mpi n ki 0 where deg pi 2ki or 2ki 1 1 i m

infinite dimensional features of matrices and pseudospectra abstract given a hilbert space operator t the level sets of function t z t z 1 1 determine the so called pseudospectra of t we set t to be zero on the spectrum of t after giving some elementary properties of t which as it seems were not noticed before we apply them to the study of the approximation we prove that for any operator t there is a sequence t n of finite matrices such that t n z tends to t z uniformly on c in this proof quasitriangular operators play a special role this is merely an existence result we do not give a concrete construction of this sequence of matrices one of our main points is to show how to use infinite dimensional operator models in order to produce examples and counterexamples in the set of finite matrices of large size in particular we get a result which means in a sense that the pseudospectrum of a nilpotent matrix can be anything one can imagine we also study the norms of the multipliers in the context of cowen douglas class operators we use these results to show that to the opposite to the function s the function s z for certain finite matrices s may oscillate arbitrarily fast even far away from the spectrum

cubic column relations in truncated moment problems for the truncated moment problem associated to a complex sequence 2n ij i j z i j 2n to have a representing measure it is necessary for the moment matrix m n to be positive semidefinite and for the algebraic variety v to satisfy rankm n cardv as well as a consistency condition the riesz functional vanishes on every polynomial of degree at most 2n that vanishes on v in previous work with l fialkow and h m moller the first named author proved that for the extremal case rankm n cardv positivity and consistency are sufficient for the existence of a representing measure in this paper we solve the truncated moment problem for cubic column relations in m 3 of the form z3 itz uz u t r we do this by checking consistency for u t in the open cone determined by 0 u t 2 u we first prove that the algebraic variety has exactly 7 points and rankm 3 7 we then apply the above mentioned result to obtain a concrete computable necessary and sufficient condition for the existence of a representing measure

non extremal sextic moment problems abstract positive semidefiniteness recursiveness and the variety condition of a moment matrix are necessary and sufficient conditions to solve the quadratic and quartic moment problems also positive semidefiniteness combined with another necessary condition consistency is a sufficient condition in the case of extremal moment problems i e when the rank of the moment matrix denoted by r and the cardinality of the associated algebraic variety denoted by v are equal however these conditions are not sufficient for non extremal sextic or higher order truncated moment problems in this paper we settle three key instances of the non extremal i e r v sextic moment problem as follows when r 7 positive semidefiniteness consistency and the variety condition guarantee the existence of a 7 atomic representing measure when r 8 we construct two determining algorithms corresponding to the cases v 9 and v to accomplish this we generalize the rank reduction technique developed in previous work where we solved the nonsingular quartic moment problem and found an explicit way to build a representing measure

dual subspaces of operators in this note we introduce some new constructions of dual spaces of operators which are of course at the same time operator spaces in the sense of pisier 2003 12 we exemplify the utility of these constructs by establishing in this more general setting a curious and little known result from the theory of dual algebras namely from chevreau and pearcy 1991 11

on quotient modules the case of arbitrary multiplicity let m be a hilbert module of holomorphic functions defined on a bounded domain cm let m0 be the submodule of functions vanishing to order k on a hypersurface z in in this paper we describe the quotient module mq

subnormality of unbounded composition operators over one circuit directed graphs exotic examples abstract a recent example of a non hyponormal injective composition operator in an l 2 space generating stieltjes moment sequences invented by three of the present authors was built over a non locally finite directed tree the main goal of this paper is to solve the problem of whether there exists such an operator over a locally finite directed graph and in the affirmative case to find the simplest possible graph with these properties simplicity refers to local valency the problem is solved affirmatively for the locally finite directed graph g 2 0 which consists of two branches and one loop the only simpler directed graph for which the problem remains unsolved consists of one branch and one loop the consistency condition the only efficient tool for verifying subnormality of unbounded composition operators is intensively studied in the context of g 2 0 which leads to a constructive method of solving the problem the method itself is partly based on transforming the krein and the friedrichs measures coming either from shifted al salam carlitz q polynomials or from a quartic birth and death process

a local theory for operator tuples in the cowen douglas class abstract we present a local theory for a commuting m tuple s s 1 s 2 s m of hilbert space operators lying in the cowen douglas class by representing s on a hilbert module m consisting of vector valued holomorphic functions over c m we identify and study the localization of s on an analytic hyper surface in c m we completely determine unitary equivalence of the localization and relate it to geometric invariants of the hermitian holomorphic vector bundle associated to s it turns out that the localization coincides with an important class of quotient hilbert modules and our result concludes its classification problem in full generality

riesz haviland criterion for incomplete data the aim of this paper is to analyze a support free version of the riesz haviland theorem proved recently by the present authors which characterizes truncations of the complex moment problem via positivity condition on appropriate families of polynomials in z and z the attention is focused on modifications of the positivity condition as well as the assumption on admissible truncations the former results in truncations for which the corresponding support free riesz haviland condition locates a representing measure on the distinguished subset of the complex plane while the latter effects a non integral variant of the riesz haviland theorem

invariant subspaces of finite codimension in banach spaces of analytic functions abstract we give a characterization of invariant subspaces of finite codimension in banach spaces of vector valued analytic functions in several variables where invariant refers to invariance under multiplication by any polynomial we obtain very weak conditions under which our characterization applies that unifies and improves a number of previous results in the vector valued case the results are new even for one complex variable as a concrete application in several variables we consider the bergman space on a strictly pseudo convex domain and we improve previous results assuming c boundary to the case of c 2 boundary

probleme des moments sur un compact de rn et decomposition de polynomes a plusieurs variables on donne la solution du probleme des moments pour un compact d interieur non vide quelconque de r n on utilise cette resolution pour obtenir un resultat de decomposition des polynomes strictement positifs sur un compact d interieur non vide

commutants and reflexivity of multiplication tuples on vector valued reproducing kernel hilbert spaces abstract motivated by the theory of weighted shifts on directed trees and its multivariable counterpart we address the question of identifying commutant and reflexivity of the multiplication d tuple m z on a reproducing kernel hilbert space h of e valued holomorphic functions on where e is a separable hilbert space and is a bounded domain in c d admitting bounded approximation by polynomials in case e is a finite dimensional cyclic subspace for m z under some natural conditions on the b e valued kernel associated with h the commutant of m z is shown to be the algebra h b e of bounded holomorphic b e valued functions on provided m z satisfies the matrix valued von neumann s inequality this generalizes a classical result of shields and wallen the case of dim e 1 and d 1 as an application we determine the commutant of a bergman shift on a leafless locally finite rooted directed tree t of finite branching index as the second main result of this paper we show that a multiplication d tuple m z on h satisfying the von neumann s inequality is reflexive this provides several new classes of examples as well as recovers special cases of various known results in one and several variables we also exhibit a family of tri diagonal b c 2 valued kernels for which the associated multiplication operators m z are non hyponormal reflexive operators with commutants equal to h b c 2 d

functional models of γn contractions and characterization of γn isometries abstract we show that a weighted bergman space on the polydisc splits up into the orthogonal direct sum of subspaces each corresponding to an irreducible representation of the symmetric group the multiplication by the n tuple of elementary symmetric functions is a n contraction on each of these subspaces a necessary condition for a commuting n tuple to be a n contraction is obtained in terms of pencil of operators we provide a model theory for n isometries a beurling lax halmos type representation for the invariant subspaces of n isometries is given

unbounded subnormal composition operators in l2 spaces abstract a novel criterion for subnormality of unbounded composition operators in l 2 spaces written in terms of measurable families of probability measures satisfying the so called consistency condition is established it becomes a new characterization of subnormality in the case of bounded composition operators pseudo moments of a measurable family of probability measures that satisfies the consistency condition are proved to be given by the radon nikodym derivatives which appear in lambert s characterization of bounded composition operators a criterion for subnormality of composition operators induced by matrices is provided the question of subnormality of composition operators over discrete measure spaces is studied two new classes of subnormal composition operators over discrete measure spaces are introduced a recent criterion for subnormality of weighted shifts on directed trees by the present authors is essentially improved in the case of rootless directed trees and nonzero weights by dropping the assumption of density of c vectors in the underlying l 2 space

the sobolev moment problem and jordan dilations abstract moment problems and orthogonal polynomials both meant in a single real variable belong to the oldest problems in classical analysis they have been developing for over a century in two parallel mostly independent streams during the last 20 years a rapid advancement of polynomials orthogonal in sobolev space has been noticed see 5 for an updated survey their moment counterpart seems not to be paid enough attention as it deserves in this paper we intend to resume the theme of 3 and also 4 and open the door for further deeper study of the problem

similarity quasisimilarity and operator factorizations we introduce and illustrate an operator factorization technique to study similarity and quasisimilarity of hilbert space operators the technique allows one to generate in a systematic way families of test operators and to check for similarity and quasisimilarity with a given model in the case of the unilateral shift u we obtain a one parameter family of nonhyponormal noncontractive shift like operators in the similarity orbit of u we also obtain new characterizations of quasisimilarity and similarity in terms of invariant operator ranges and conditions for spectral and essential spectral inclusions

homogeneous vector bundles and intertwining operators for symmetric domains the main features of homogeneous cowen douglas operators well known for the unit disk are generalised to the setting of hermitian bounded symmetric domains of arbitrary rank c 2016 elsevier inc all rights reserved

unitary equivalence of operator valued multishifts abstract we systematically study various aspects of operator valued multishifts beginning with basic properties we show that the class of multishifts on the directed cartesian product of rooted directed trees is contained in that of operator valued multishifts further we establish circularity analyticity and wandering subspace property of these multishifts in the rest part of the paper we study the function theoretic behaviour of operator valued multishifts we determine the bounded point evaluation reproducing kernel structure and the unitary equivalence of operator valued multishifts with invertible operator weights in contrast with a result of lubin it appears that the set of all bounded point evaluations of an operator valued multishift may be properly contained in the joint point spectrum of the adjoint of underlying multishift

the core variety of a multisequence in the truncated moment problem abstract let m i i z n i m 0 0 denote a real n dimensional multisequence of finite degree m the truncated moment problem concerns the existence of a positive borel measure supported in r n such that 0 1 i r n x i d i z n i m we associate to 2 d an algebraic variety in r n called the core variety v v the core variety contains the support of each representing measure we show that if v is nonempty then 2 d 1 has a representing measure moreover if v is a nonempty compact or determining set then 2 d has a representing measure we also use the core variety to exhibit a sequence with positive definite moment matrix and positive riesz functional which fails to have a representing measure

unbounded extensions and operator moment problems abstract extension results expressed in terms of complete boundedness leading to necessary and sufficient conditions for the solvability of power moment problems with unbounded operator data are given as an application necessary and sufficient conditions for the existence of selfadjoint and normal extensions for some classes of commuting tuples of unbounded linear operators are obtained

eisenstein congruence on unitary groups and iwasawa main conjectures for cm fields the purpose of this article is to prove iwasawa main conjecture for cm fields in certain cases through an extensive study on the divisibility relation between p adic l functions for cm fields and eisenstein ideals of unitary groups of degree three

on the sum of two subnormal kernels abstract we show by means of a class of examples that if k 1 and k 2 are two positive definite kernels on the unit disc such that the multiplication by the coordinate function on the corresponding reproducing kernel hilbert space is subnormal then the multiplication operator on the hilbert space determined by their sum k 1 k 2 need not be subnormal this settles a recent conjecture of gregory t adams nathan s feldman and paul j mcguire in the negative we also discuss some cases for which the answer is affirmative

an r t theorem for imaginary quadratic fields we prove the modularity of certain residually reducible p adic galois representations of an imaginary quadratic field assuming the uniqueness of the residual representation we obtain an r t theorem using a new commutative algebra criterion that might be of independent interest to apply the criterion one needs to show that the quotient of the universal deformation ring r by its ideal of reducibility is cyclic artinian of order no greater than the order of the congruence module t j where j is an eisenstein ideal in the local hecke algebra t the inequality is proven by applying the main conjecture of iwasawa theory for hecke characters and using a result of berger compos math 145 3 603 632 2009 this strengthens our previous result berger and klosin j inst math jussieu 8 4 669 692 2009 to include the cases of an arbitrary p adic valuation of the l value in particular cases when r is not a discrete valuation ring as a consequence we show that the eisenstein ideal is principal and that t is a complete intersection

on the structure of contraction operators with applications to invariant subspaces on ameliore certaines conditions suffisantes pour un membre de la classe a d 0 on obtient de nouvelles conditions suffisantes pour qu une contraction sur un espace de hilbert dont le spectre contient le cercle unite ait des sous espaces invariants non triviaux

curvature invariant and generalized canonical operator models ii one can view contraction operators given by a canonical model of sz nagy and foias as being defined by a quotient module where the basic building blocks are hardy spaces i n this note we generalize this framework to allow the bergman and weighted bergman spaces as building blocks but restricting attention to the case in which the operator obtained is in the cowen douglas class and requiring the multiplicity to be one w e view the classification of such operators in the context of complex geometry and obtain a complete classification up to unitary equivalence of them in terms of their associated vector bundles and their curvatures

sampling and prefiltering effects on blind equalizer design in the development of equalization algorithms for unknown channels the effects of the sampling rate and the analog receive prefilter prior to discretization of the received signal are often overlooked in this paper these effects are investigated the relationship between the fractionally spaced output samples of a noise limiting prefilter and the symbol spaced output samples of a matched filter is studied for both the time invariant and the time varying channels it is shown that the prefilter and the sampling rate can have significant effects on blind equalization algorithms thus this paper provides a common framework for comparing different blind algorithms that are studied in the literature with different sampling rates a case study of the well known subspace method for blind channel identification is presented the effects of the noise color due to the prefilter on equalizers is investigated and the sensitivity of the truncation of the overall channel impulse response in terms of the mean squared error mse performance criterion is investigated through numerical examples

classification of quasi homogeneous holomorphic curves and operators in the cowen douglas class abstract in this paper we study quasi homogeneous operators which include the homogeneous operators in the cowen douglas class we give two separate theorems describing canonical models with respect to equivalence under unitary and invertible operators respectively for these operators using techniques from complex geometry this considerably extends the similarity and unitary classification of homogeneous operators in the cowen douglas class obtained recently by the last author and a koranyi in a significant generalization of the properties of the homogeneous operators we show that quasi homogeneous operators are irreducible and determine which of them are strongly irreducible applications include the equality of the topological and algebraic k group of a quasi homogeneous operator and an affirmative answer to a well known question of halmos

manifolds of hilbert space projections the hardy space h2 for the upper half plane together with a multiplicative group of unimodular functions u exp i 11 nn with n gives rise to a manifold of orthogonal projections for the subspaces u h2 of l2 for classes of admissible functions i the strong operator topology closures of and are determined explicitly as various n balls and n spheres the arguments used are direct and rely on the analysis of oscillatory integrals e m stein harmonic analysis real variable methods orthogonality and oscillatory integrals princeton mathematical series 43 princeton university press princeton nj 1993 and hilbert space geometry some classes of these closed projection manifolds are classified up to unitary equivalence in particular the fourier plancherel 2 sphere and the hyperbolic 3 sphere of katavolos and power a katavolos and s c power translation and dilation invariant subspaces of l2 j reine angew math 552 2002 101 129 appear as distinguished special cases admitting non trivial unitary automorphism groups which are explicitly described

a positivstellensatz for non commutative polynomials a non commutative polynomial which is positive on a bounded semi algebraic set of operators has a weighted sum of squares representation this positivstellensatz parallels similar results in the commutative case a broader issue is to what extent does real semi algebraic geometry extend to non commutative polynomials our strict positivstellensatz is positive news on the opposite extreme from strict positivity would be a real nullstellensatz we give an example which shows that there is no non commutative real nullstellensatz along certain lines however we include a successful type of non commutative nullstellensatz proved by george bergman

how can we construct abelian galois extensions of basic number elds recall the almost tautological but very useful way we have of dealing with an irreducible polynomial over a field for example in the case of x5 x 1 irreducible over the rational field q we happily adjoin a root to our base field by merely forming l the quotient of the polynomial ring q x modulo the ideal generated by x5 x 1 then l is a field of algebraic numbers and the image of x is indeed a root of x5 x 1 in l

the complex moment problem and subnormality a polar decomposition approach abstract it has been known that positive definiteness does not guarantee a bisequence to be a complex moment however it turns out that positive definite extendibility does theorems 1 and 22 and this is the main theme of this paper the main tool is generally understood polar decomposition to strengthen applicability of our approach we work out a criterion for positive definite extendibility in a fairly wide context theorems 9 and 29 all this enables us to prove characterizations of subnormality of unbounded operators having invariant domain theorems 37 and 39 and their further applications theorems 41 and 43 and a description of the complex moment problem on real algebraic curves theorems 52 and 56 the latter question is completed in the appendix in which we relate the complex moment problem to the two dimensional real one with emphasis on real algebraic sets

on reducing submodules of hilbert modules with g n invariant kernels fix a bounded domain omega subset of c n and a positive definite kernel k on omega both invariant under g n the permutation group on n symbols let h subset of hol omega be the hilbert module determined by k we show that h splits into orthogonal direct sum of subspaces pph indexed by the partitions p of n we prove that each submodule pph is a locally free hilbert module of rank equal to square of the dimension chi p 1 of the irreducible representation corresponding to p given two partitions p and q we show that if chi p 1 not equal chi q 1 then the sub modules pph and pqh are not unitarily equivalent we prove that if h is a contractive analytic hilbert module on omega then the taylor joint spectrum of the n tuple of multiplication operators by elementary symmetric polynomials on pph is clos s omega where s c n c n is the symmetrization map it is then shown that this commuting tuple of operators defines a contractive homomorphism of the ring of symmetric polynomials cz gn in n variables equipped with the sup norm on clos s omega c 2018 elsevier inc all rights reserved

on optimal detection of band limited pam signals with excess bandwidth pam data transmission receivers accomplishing maximum likelihood sequence detection mlsd usually require a matched filter prefilter a sampler at the symbol rate and a viterbi algorithm detector when the channel is unknown or slowly changing one must use an adaptive matched filter prefilter we examine an alternative optimum receiver whose optimality is independent of the matched filter prefilter and which is applicable when the channel is effectively band limited the sampler in the proposed receiver operates at a rate faster than the data symbol rate enabling one to replace the matched filter by a fixed low pass filter and still ensure that the maximum likelihood detector is supplied with a set of sufficient statistics it is shown that the matched filter is incorporated within a modified viterbi detector without increasing the number of states in the algorithm although the viterbi detector must perform computations at approximately twice the usual rate simulations support the optimality of the new receiver and quantitatively indicate the degradation in performance experienced by some adaptive receivers previously proposed

commutative algebras of unbounded operators abstract we consider algebras u of unbounded operators defined on a common invariant dense domain d in a hilbert space h we assume that u is generated by a finite number of operators s1 sd satisfying the inequality x s x x s x x 0 for all finite sets of vectors x indexed by 1 d i 0 1 1 i d where s s 1 1 s d d and denotes the inner product in h we show that every such algebra dilates to a commutative algebra in a generally bigger hilbert space the latter algebra is generated by commuting formally normal extension operators n1 nd such that sjx njx x d 1 j d moreover the adjoint operators n j are represented as multiplication operators on a quotient of the space of d valued polynomials in complex variables z1 zd c d n j z j z d z j u z j z d if it is further assumed that d contains a dense space of vectors analytic for each of the operators sj then we prove that the nj s are essentially normal and there is a spectral measure e on the product of the spectrum of the closed normal operators n j such that n i f de and sjx jde x for x d as an application we consider representations of the canonical commutation relations in d degrees of freedom if p1 pd q1 qd denote the momentum resp position operators and sj pj iqj we show that s1 sd admits a representation as above we also show using our analytic vector theorem that the corresponding extension operators n 1 n d are commuting and normal for the schrodinger representation finally we calculate the spectral representation for the operators n j and prove absolute continuity and uniform multiplicity equal infinity the exposition of the paper begins with the case d 1 this is the unbounded version of the subnormal operators which have been studied extensively in the past in the case of bounded operators we stress the differences between the theory for the bounded and the unbounded case even in the case d 1 the applications of the unbounded theory are surprising

homogeneous operators on hilbert spaces of holomorphic functions i in this paper we construct a large class of multiplication operators on reproducing kernel hilbert spaces which are homogeneous with respect to the action of the m o bius group consisting of bi holomorphic automorphisms of the unit disc mathbb d for every m in n we have a family of operators depending on m 1 positive real parameters the kernel function is calculated explicitly it is proved that each of these operators is bounded lies in the cowen douglas class of mathbb d and is irreducible these operators are shown to be mutually pairwise unitarily inequivalent

on the main conjecture for cm fields the aim of this work is to prove a divisibility relation toward the main conjecture for cm fields our main tool is the study of congruences between an eisenstein series and cusp forms on the unitary group gu 2 1 we introduce an eisenstein ideal in the nearly ordinary universal hecke algebra for gu 2 1 and show that it divides the characteristic ideal of the cm iwasawa module

rigidity of the flag structure for a class of cowen douglas operators the explicit description of irreducible homogeneous operators in the cowen douglas class and the localization of hilbert modules naturally leads to the definition of a smaller class possessing a flag structure these operators are shown to be irreducible it is also shown that the flag structure is rigid that is the unitary equivalence class of the operator and the flag structure determine each other a complete set of unitary invariants which are somewhat more tractable than those of an arbitrary operator in the cowen douglas class is obtained c 2017 elsevier inc all rights reserved

bounded modules extremal problems and a curvature inequality abstract in this paper we study certain finite dimensional hilbert modules over the function algebra a c n these modules appear as localizations of a cowen douglas operator we show that these modules are always bounded where the bound is related to the solution of an extremal problem in particular we obtain necessary sufficient conditions for such a module to be contractive we apply the above results to produce an example of a contractive module over a b 2 which is not completely contractive

fiber dimension for invariant subspaces abstract in this paper we study the fiber dimension of invariant subspaces for a large class of operators we define a class of invariant subspaces called cf subspaces which are related to the codimension one property we obtain several characterizations of cf subspaces including one in terms of samuel multiplicity other new findings include 1 a lattice additive formula and its applications section 4 2 a new concept of absorbance which describes a rough containment relation for invariant subspaces section 5 3 the existence of a unique smallest cf subspace containing an arbitrary invariant subspace and preserving the fiber dimension section 6

on the structure of contraction operators ii soit 7b h un espace de hilbert complexe separable de dimension infinie et 7b l 7b h l algebre de tous les operateurs lineaires bornes sur 7b h soit d le disque unite ouvert dans c d et n est l ensemble des entiers positifs il existe r 6 tel que chaque contraction t dans 7b l 7b h avec c t soit a un sous espace hyperinvariant non trivial soit appartient a la classe a 1 r

the curvature invariant for a class of homogeneous operators for an operator t in the class b n introduced by cowen and douglas the simultaneous unitary equivalence class of the curvature and the covariant derivatives up to a certain order of the corresponding bundle e t determine the unitary equivalence class of the operator t in a subsequent paper the authors ask if the simultaneous unitary equivalence class of the curvature and these covariant derivatives are necessary to determine the unitary equivalence class of the operator t is an element of b n here we show that some of the covariant derivatives are necessary our examples consist of homogeneous operators in b n for homogeneous operators the simultaneous unitary equivalence class of the curvature and all its covariant derivatives at any point w in the unit disc are determined from the simultaneous unitary equivalence class at 0 this shows that it is enough to calculate all the invariants and compare them at just one point say 0 these calculations are then carried out in number of examples one of our main results is that the curvature along with its covariant derivative of order 0 1 at 0 determines the equivalence class of generic homogeneous hermitian holomorphic vector bundles over the unit disc

the moment problem on compact semi algebraic sets in this chapter we begin the study of the multidimensional moment problem the passage to dimensions d 2 brings new difficulties and unexpected phenomena in sect 3 2 we derived solvability criteria of the moment problem on intervals in terms of positivity conditions it seems to be natural to look for similar characterizations in higher dimensions as well this leads us immediately into the realm of real algebraic geometry and to descriptions of positive polynomials on semi algebraic sets in this chapter we treat this approach for basic closed compact semi algebraic subsets of mathbb r d it turns out that for such sets there is a close interaction between the moment problem and positivstellensatze for strictly positive polynomials

equivalence of quotient hilbert modules ii for any open connected and bounded set c m let a be a natural function algebra consisting of functions holomorphic on let m be a hilbert module over the algebra a and m0 m be the submodule of functions vanishing to order k on a hypersurface z recently the authors have obtained an explicit complete set of unitary invariants for the quotient module q m m0 in the case of k 2 in this paper we relate these invariants to familiar notions from complex geometry we also find a complete set of unitary invariants for the general case we discuss many concrete examples in this setting as an application of our equivalence results we characterise certain homogeneous hilbert modules over the bi disc algebra one source of fascination in the study of operator theory is the wide variety of connections made with other branches of mathematics techniques from algebra topology geometry and analysis are used to understand bounded linear operators on hilbert space and in many instances the behavior and properties of the operators can be used to illustrate critical features and aspects of the other fields this is particularly true in the case of multivariate operator theory that is when several operators or an algebra of operators is studied here the setting and results from these other areas can be quite sophisticated and the techniques used to understand multivariate operator theory often require additional development such is the focus of this paper although the spectral theorem is a key tool in the study of self adjoint and normal opera tors there are large and important classes of naturally occurring operators to which this theory doesn t apply examples illustrating such phenomena can be obtained by considering multipli cation operators on spaces of holomorphic functions on some domain in c m for domains in c one is in the realm of single operator theory while it is multivariate operator theory for m 1 if one considers the unit ball b m in c m and the bergman space a 2 b m for it one obtains a

unitary invariants for hilbert modules of finite rank we associate a sheaf model to a class of hilbert modules satisfying a natural finiteness condition it is obtained as the dual to a linear system of hermitian vector spaces in the sense of grothendieck a refined notion of curvature is derived from this construction leading to a new unitary invariant for the hilbert module a division problem with bounds originating in douady s privilege is related to this framework a series of concrete computations illustrate the abstract concepts of the paper

fredholm and invertible tuples of operators the deformation problem using j l taylor s definition of joint spectrum we study fredholm and invertible tuples of operators on a hilbert space we give the foundations for a several variables theory including a natural generalization of atkinson s theorem and an index which well behaves we obtain a characterization of joint invertibility in terms of a single operator and study the main examples at length we then consider the deformation problem and solve it for the class of almost doubly commuting fredholm pairs with a semi fredholm coordinate 1 introduction 1 let t be a bounded linear operator on a banach space t is said to be invertible if there exists an operator s on such that ts st 1 the identity operator on 9c by the open mapping theorem this is equivalent to ker t 0 and r t range of t the last formulation does not rely upon the existence of an inverse for t but rather on the action of the operator t when t is replaced by an tuple of commuting operators several definitions of nonsingular ity exist j l taylor 19 has obtained one which reflects the actions of the operators by considering the koszul complex associated with the tuple 2 in this paper we develop a general several variables theory on the basis of taylor s work and study commuting and almost commuting commuting mod ulo the compacts tuples of operators on a hilbert space we obtain a characterization of joint invertibility in terms of the invertibility of a single operator which is essential for our approach from that we get a number of corollaries which generalize nicely the known elementary results in one variable at the same time the referred characterization allows us to define a continuous invariant under compact perturbations integer valued index on the class of fred holm tuples those almost commuting tuples which are invertible in the calkin algebra this index extends the classical one for fredholm operators we prove that an almost commuting tuple of essentially normal operators with all commu tators in trace class has index zero 2 and that a natural generalization of atkinson s theorem holds for tuples

orthogonality of analytic polynomials a little step further from the constellation mentioned in jones and njastad j comput appl math 105 1999 51 91 we have chosen orthogonality of polynomials and moment problems enriching them with operator theory apparatus thus this essay resumes the theme of szafraniec j comput appl math 49 1993 255 and culminates in updating it with the results of stochel and szafraniec j funct anal 159 1998 432

extending positive definiteness the main result of this paper gives criteria for extendibility of mappings defined on symmetric subsets of semigroups to positive definite ones by specifying the mappings in question we obtain new solutions of relevant issues in harmonic analysis concerning truncations of some important multivariate moment problems like complex two sided complex and multidimensional trigonometric moment problems in addition unbounded subnormality and existence of unitary power dilation of several contractions is treated as an application of our general scheme

the fredholm index of a pair of commuting operators ii this paper concerns fredholm theory in several variables and its applications to hilbert spaces of analytic functions one feature is the introduction of ideas from commutative algebra to operator theory specifically we introduce a method to calculate the fredholm index of a pair of commuting operators to achieve this we define and study the hilbert space analogs of samuel multiplicities in commutative algebra then the theory is applied to the symmetric fock space in particular our results imply a satisfactory answer to arveson s program on developing a fredholm theory for pure d contractions when d 2 including both the fredholmness problem and the calculation of indices we also show that arveson s curvature invariant is in fact always equal to the samuel multiplicity for an arbitrary pure d contraction with finite defect rank it follows that the curvature is a similarity invariant

mlse and soft output equalization for trellis coded continuous phase modulation this paper presents two equalizer structures for trellis coded continuous phase modulation tc cpm on multipath fading intersymbol interference isi channels an equivalent discrete time dt model is developed by combining the tapped delay line tdl model of the frequency selective channel and by oversampling at the receiver the noninterleaved fractionally spaced maximum likelihood sequence estimation mlse equalizer performs continuous phase modulation cpm demodulation trellis coded modulation tcm decoding and channel equalization by exploiting the finite state nature of the isi corrupted tc cpm signal both simulation and analytical results show diversity like improvement when performing joint mlse decoding and equalization for the interleaved soft output equalizer the soft symbol metric is delivered to the tcm decoder by using a forward and backward recursion algorithm three variants of the soft output equalizer are examined we conclude that the backward recursion is essential to partial response cpm schemes and with moderate complexity the soft output equalizer can have a substantial advantage over a noninterleaved mlse equalizer

on deformation rings of residually reducible galois representations and r t theorems we introduce a new method of proof for r t theorems in the residually reducible case we study the crystalline universal deformation ring r and its ideal of reducibility i of a mod p galois representation 0 of dimension n whose semisimplification is the direct sum of two absolutely irreducible mutually non isomorphic constituents 1 and 2 under some assumptions on selmer groups associated with 1 and 2 we show that r i is cyclic and often finite using ideas and results of but somewhat different assumptions from bellaiche and chenevier we prove that i is principal for essentially self dual representations and deduce statements about the structure of r using a new commutative algebra criterion we show that given enough information on the hecke side one gets an r t theorem we then apply the technique to modularity problems for 2 dimensional representations over an imaginary quadratic field and a 4 dimensional representation over q

a duality proof of tchakaloff s theorem abstract tchakaloff s theorem establishes the existence of a quadrature rule of prescribed degree relative to a positive compactly supported measure that is absolutely continuous with respect to lebesgue measure on r d subsequent extensions were obtained by mysovskikh and by putinar we provide new proofs and partial extensions of these results based on duality techniques utilized by stochel we also obtain new uniqueness criteria in the truncated complex moment problem

solution of the truncated moment problem with variety y x 3 we show that positivity consistency and the variety condition which are sufficient to solve the truncated moment problem on planar curves of degree 2 are not sufficient for curves of higher degree using new partly algorithmic conditions based on positive moment matrix extensions we present a concrete solution to the truncated moment problem on the curve y x 3 we also use moment matrix extensions to solve in a less concrete sense truncated moment problems on curves of the form y g x and yg x 1 g x leading to degree bounded weighted sum of squares representations for polynomials which are strictly positive on such curves

a subnormal weighted shift on a directed tree whose nth power has trivial domain abstract it is shown that for any positive integer n there exists a subnormal weighted shift on a directed tree whose nth power is closed and densely defined while its n 1 th power has trivial domain similar result for composition operators in l 2 spaces is established

a contribution to the structure theory of operators in the class a soit 7b h un espace de hilbert separable et soit t une contraction agissant sur 7b h on suppose que t est absolument continu soit 7b a t l etoile fermee algebre faible engendree par t si t a on dit que t appartient a la classe a 1 si pour chaque fonctionnelle etoile continue faible sur 7b a t il existe des vecteurs n y 7b h satisfaisant a a 7b a t on montre que chaque operateur t tel que t a et soit t n 0 soit t n o avec 1 n appartient a a 1

composition operators on hilbert spaces of entire functions with analytic symbols abstract composition operators with analytic symbols on some reproducing kernel hilbert spaces of entire functions on a complex hilbert space are studied the questions of their boundedness seminormality and positivity are investigated it is proved that if such an operator is bounded then its symbol is a polynomial of degree at most 1 i e it is an affine mapping fock s type model for composition operators with linear symbols is established as a consequence explicit formulas for their polar decomposition aluthge transform and powers with positive real exponents are provided the theorem of carswell maccluer and schuster is generalized to the case of segal bargmann spaces of infinite order some related questions are also discussed

a unitary invariant for hyponormal operators abstract several complete unitary invariants for a pure hyponormal operator are described and related to already known invariants among them an operator valued distribution supported by the spectrum has a distinguished position the inverse problems and the relations between these invariants are also discussed parts of this paper were motivated by the recent work of k clancey

on intertwining operators via reproducing kernels abstract in this note we investigate operators intertwining the coordinate multiplication between functional hilbert spaces in terms of their matrix valued reproducing kernel functions which extends the work of curto and salinas 1984 4 on unitary intertwining operators

on residually reducible representations on local rings let a be a local artinian ring with maximal ideal m and residual field k let r be an a algebra we mean by an n dimensional a representa tion of r any homomorphism of a algebra r from r to m a for such n a representation we denote by r the residual representation with values in m k it is proven by carayol that such a representation if r is absolutely n irreducible is completely determined by its trace in the reducible case one cannot generalize this theorem without assuming more hypothesis see w x the counterexample given in 1 the purpose of this note is to give a generalization in the reducible case it is the best generalization one can get see remarks

the classical moment problem as a self adjoint finite difference operator abstract this is a comprehensive exposition of the classical moment problem using methods from the theory of finite difference operators among the advantages of this approach is that the nevanlinna functions appear as elements of a transfer matrix and convergence of pade approximants appears as the strong resolvent convergence of finite matrix approximations to a jacobi matrix as a bonus of this we obtain new results on the convergence of certain pade approximants for series of hamburger

subnormal operators whose adjoints have rich point spectrum a generalized version of the glauber klauder basic formula of quantum optics is shown to be valid for any cyclic subnormal operator s whose adjoint has a rich point spectrum p s in the sense that a semispectral measure of s vanishes on c p s it is exhibited that such operators always have analytic models the point spectrum of the adjoint of a subnormal operator which satisfies a generalized version of the glauber klauder formula is proved to be rich in the above sense

some thoughts on ando s theorem and parrott s example in this short note we present an elementary proof of ando s theorem within a restricted class p of homomorphisms modeled after parrott s example we also show by explicit estimation that the cb norm of the contractive homomorphism of the tri disc algebra induced by the commuting triple of parrott exceeds 1 indeed we construct a polynomial p with matrix coefficients with the property p p in particular we show that there are contractive homomorphisms of the tri disc algebra which are not even 2 contractive

hankel vector moment sequences and the non tangential regularity at infinity of two variable pick functions a pick function of d variables is a holomorphic map from d to where is the upper halfplane some pick functions of one variable have an asymptotic expansion at infinity a power series n 1 nz n with real numbers n that gives an asymptotic expansion on non tangential approach regions to infinity in 1921 h hamburger characterized which sequences n can occur we give an extension of hamburger s results to pick functions of two variables

reinhardt domains boundary geometry and toeplitz c algebras abstract in this paper we have found explicitly how the boundary geometry of a reinhardt domain in c 2 determines the structure of its toeplitz c algebra more precisely our main result is an explicit simple algorithm to describe the structure of the toeplitz c algebra of a reinhardt domain d in c 2 satisfying some mild boundary condition in terms of rotation c algebras based on the degree of contact of the boundary curve of c the logarithmic domain of d at each point of intersection with the linear faces of the convex hull of c and the slopes of these faces a consequence of this result is that the toeplitz c algebras t d and t d of d and its pseudoconvex hull d are rarely isomorphic but are always of the same type i e either both are of type i or both are not of type i in other words the isomorphism class of t d is usually changed under taking pseudoconvex hull but the type of t d is not affected