isometric dilations for infinite sequences of noncommuting operators this paper develops a dilation theory for t n l an infinite sequence of noncommuting operators on a hilbert space when the matrix t1 t2 is a contraction a wold decomposition for an infinite sequence of isometries with orthogonal final spaces and a minimal isometric dilation for tn i are obtained some theorems on the geometric structure of the space of the minimal isometric dilation and some consequences are given this results are used to extend the sz nagy foia lifting theorem to this noncommutative setting this paper is a continuation of 5 and develops a dilation theory for an infinite sequence tn n of noncommuting operators on a hilbert space when en 1 tn tn i i is the identity on s many of the results and techniques in dilation theory for one operator 8 and also for two operators 3 4 are extended to this setting first we extend wold decomposition 8 4 to the case of an infinite sequence vn i of isometries with orthogonal final spaces in 2 we obtain a minimal isometric dilation for tn 1 by extending the schaffer construction in 6 4 using these results we give some theorems on the geometric structure of the space of the minimal isometric dilation finally we give some sufficient conditions on a sequence t7 n to be simultaneously quasi similar to a sequence rn n i of isometries on a hilbert space x with en rnrn n ix in 3 we use the above mentioned theorems to obtain the sz nagy foia5 lifting theorem 7 8 1 4 in our setting in a subsequent paper we will use the results of this paper for studying the characteristic function associated to a sequence tn lo 1 with ez 1 t t i throughout this paper a stands for the set 1 2 k k e n or the set n 1 2 received by the editors september 1 1987 1980 mathematics subject classification 1985 revision primary 47a20 secondary 47a45

models for n tuples of noncommuting operators abstract this paper proves versions of the rota model theorem the de branges rovnyak model theorem and the coisometric extension theorem for n tuples of not necessarily commuting operators this generalizes the work of a e frazho j funct anal 48 1982 1 11 for pairs of operators the methods involve applying the single operator results to matrices of operators

invariant subspaces and hyper reflexivity for free semigroup algebras in this paper we obtain a complete description of the invariant subspace structure of an interesting new class of algebras which we call free semigroup algebras this enables us to prove that they are reflexive and moreover to obtain a quantitative measure of the distance to these algebras in terms of the invariant subspaces such algebras are called hyper reflexive this property is very strong but it has been established in only a very few cases moreover the prototypes of this class of algebras are the natural candidate for a non commutative analytic toeplitz algebra on n variables the case we make for this analogy is very compelling in particular in this paper the key to the invariant subspace analysis is a good analogue of the beurling theorem for invariant subspaces of the unilateral shift this leads to a notion of inner outer factorization in these algebras in a sequel to this paper 13 we add to this evidence by showing that there is a natural homomorphism of the automorphism group onto the group of conformal automorphisms of the ball in cn a free semigroup algebra is the weak operator topology closed algebra generated by a set s1 sn of isometries with pairwise orthogonal ranges these conditions are described algebraically by s i sj iji for 1 i j n f

pure e0 semigroups and absorbing states an e0 semigroup acting on is called pure if its tail von neumann algebra is trivial in the sense that we determine all pure e0 semigroups which have a weakly continuous invariant state and which are minimal in an appropriate sense in such cases the dynamics of the state space must stabilize as follows for every normal state of there is convergence to equilibrium in the trace norm a normal state with this property is called an absorbing state for

absolute continuity for commuting row contractions abstract absolutely continuous commuting row contractions admit a weak continuous functional calculus building on recent work describing the first and second dual spaces of the closure of the polynomial multipliers on the drury arveson space we give a complete characterization of these commuting row contractions in measure theoretic terms we also establish that completely non unitary row contractions are necessarily absolutely continuous in direct parallel with the case of a single contraction finally we consider refinements of this question for row contractions that are annihilated by a given ideal

characterization of large price variations in financial markets statistics of drawdowns loss from the last local maximum to the next local minimum plays an important role in risk assessment of investment strategies as they incorporate higher two order correlations they offer a better measure of real market risks than the variance or other cumulants of daily or some other fixed time scale of returns previous results have shown that the vast majority of drawdowns occurring on the major financial markets have a distribution which is well represented by a stretched exponential while the largest drawdowns are occurring with a significantly larger rate than predicted by the bulk of the distribution and should thus be characterized as outliers eur phys j b 1 1998 141 j risk 2001 in the present analysis the definition of drawdowns is generalized to coarse grained drawdowns or so called e drawdowns and a link between such e outliers and preceding log periodic power law bubbles previously identified quantitative finance 1 2001 452 is established

subalgebras of c algebras iii multivariable operator theory a d contraction is a d tuple t1 td of mutually commuting operators acting on a common hilbert space h such that t1 1 t2 2 td d 1 2 d for all 1 2 d h these are the higher dimensional counterparts of contractions we show that many of the operator theoretic aspects of function theory in the unit disk generalize to the unit ball bd in complex d space including von neumann s inequality and the model theory of contractions these results depend on properties of the d shift a distinguished d contraction which acts on a new h2 space associated with bd and which is the higher dimensional counterpart of the unilateral shift h 2 and the d shift are highly unique indeed by exploiting the noncommutative choquet boundary of the d shift relative to its generated c algebra we find that there is more uniqueness in dimension d 2 than there is in dimension one

large deviations and portfolio optimization abstract risk control and optimal diversification constitute a major focus in the finance and insurance industries as well as more or less consciously in our everyday life we present a discussion of the characterization of risks and of the optimization of portfolios that starts from a simple illustrative model and ends by a general functional integral formulation a major item is that risk usually thought of as one dimensional in the conventional mean variance approach has to be addressed by the full distribution of losses furthermore the time horizon of the investment is shown to play a major role we show the importance of accounting for large fluctuations and use the theory of cramer for large deviations in this context we first treat a simple model with a single risky asset that exemplifies the distinction between the average return and the typical return and the role of large deviations in multiplicative processes and the different optimal strategies for the investors depending on their size we then analyze the case of assets whose price variations are distributed according to exponential laws a situation that is found to describe daily price variations reasonably well several portfolio optimization strategies are presented that aim at controlling large risks we end by extending the standard mean variance portfolio optimization theory first within the quasi gaussian approximation and then using a general formulation for non gaussian correlated assets in terms of the formalism of functional integrals developed in the field theory of critical phenomena

the index of a quantum dynamical semigroup a numerical index is introduced for semigroups of completely positive maps of b h which generalizes the index ofe0 semigroups it is shown that the index of a unital completely positive semigroup agrees with the index of its dilation to ane0 semigroup provided that the dilation isminimal

the algebraic structure of non commutative analytic toeplitz algebras the non commutative analytic toeplitz algebra is the wot closed algebra generated by the left regular representation of the free semigroup on n generators we develop a detailed picture of the algebraic structure of this algebra in particular we show that there is a canonical homomorphism of the automorphism group onto the group of conformal automorphisms of the complex n ball the k dimensional representations form a generalized maximal ideal space with a canonical surjection onto the ball of k kn matrices which is a homeomorphism over the open ball analogous to the fibration of the maximal ideal space of h over the unit disk in 6 17 18 20 a good case is made that the appropriate analogue for the analytic toeplitz algebra in n non commuting variables is the wotclosed algebra generated by the left regular representation of the free semigroup on n generators the papers cited obtain a compelling analogue of beurling s theorem and inner outer factorization in this paper we add further evidence the main result is a short exact sequence determined by a canonical homomorphism of the automorphism group onto this algebra onto the group of conformal automorphisms of the unit ball of cn the kernel is the subgroup of quasi inner automorphisms which are trivial modulo the wot closed commutator ideal additional evidence of analytic properties comes from the structure of k dimensional completely contractive representations which have a structure very similar to the fibration of the maximal ideal space of h over the unit disk an important tool in our analysis is a detailed structure theory for wot closed right ideals curiously left ideals remain more obscure the non commutative analytic toeplitz algebra ln is determined by the left regular representation of the free semigroup fn on n generators z1 zn which acts on 2 fn by w v wv for v w in fn in particular the algebra ln is the unital wot closed algebra generated by the isometries li zi for 1 i n this algebra and its norm closed version the noncommutative disk algebra were introduced by popescu 19 in an abstract sense in connection with a non commutative von neumann inequality and 1991 mathematics subject classification 47d25 march 9 1997 october 9 1997 final draft first author partially supported by an nserc grant and a killam research fellowship second author partially supported by an nsf grant

predicting critical crashes a new restriction for the free variables abstract several authors have noticed the signature of log periodic oscillations prior to large stock market crashes unfortunately the prediction of crashes with this method is difficult since good fits of the corresponding log periodic equation to stock market prices are also observed in quiet times we deduce a new inequality among the free variables in this equation that must be satisfied before a crash this inequality alone yields crash predictions with a 25 success rate for the dow jones index this compares to a 9 success rate obtained by previous approaches combining our method with previous ones we obtain a success rate of 54

on c initial spaces abstract the concept of c initial topology associated with a completely induced fuzzy topological space 4 is introduced and some of its properties are investigated the relationship between the topologies of c initial space and an initial space 8 is shown it is proved that the concepts of super continuity continuity continuity and almost continuity are equivalent in case when the domain and the range of the function are both c initial topological spaces

free holomorphic functions on the unit ball of b h n abstract in this paper we continue the study of free holomorphic functions on the noncommutative ball b h n 1 x 1 x n b h n x 1 x 1 x n x n 1 2 1 where b h is the algebra of all bounded linear operators on a hilbert space h and n 1 2 or n several classical results from complex analysis have free analogues in our noncommutative setting we prove a maximum principle a naimark type representation theorem and a vitali convergence theorem for free holomorphic functions with operator valued coefficients we introduce the class of free holomorphic functions with the radial infimum property and study it in connection with factorizations and noncommutative generalizations of some classical inequalities obtained by schwarz and harnack the borel caratheodory theorem is extended to our noncommutative setting using a noncommutative generalization of schwarz s lemma and basic facts concerning the free holomorphic automorphisms of the noncommutative ball b h n 1 we obtain an analogue of julia s lemma for free holomorphic functions f b h n 1 b h m 1 we also obtain pick julia theorems for free holomorphic functions with operator valued coefficients we provide a noncommutative generalization of a classical inequality due to lindelof which turns out to be sharper then the noncommutative von neumann inequality finally we introduce a pseudohyperbolic metric on b h n 1 which is invariant under the action of the free holomorphic automorphism group of b h n 1 and turns out to be a noncommutative extension of the pseudohyperbolic distance on b n the open unit ball of c n in this setting we obtain a schwarz pick type lemma we also provide commutative versions of these results for operator valued multipliers of the drury arveson space

induced fuzzy supra topological spaces abstract the aim of this paper is to introduce and to study the concepts of induced fuzzy supra topological spaces and s lower semi continuous functions s lower semi continuous functions turn out to be the natural tool for studying the induced fuzzy supra topological spaces

lppls bubble indicators over two centuries of the s p 500 index the aim of this paper is to present novel tests for the early causal diagnostic of positive and negative bubbles in the s p 500 index and the detection of end of bubble signals with their corresponding confidence levels we use monthly s p 500 data covering the period from august 1791 to august 2014 this study is the first work in the literature showing the possibility to develop reliable ex ante diagnostics of the frequent regime shifts over two centuries of data we show that the ds lppls log periodic power law singularity approach successfully diagnoses positive and negative bubbles constructs efficient end of bubble signals for all of the well documented bubbles and obtains for the first time new statistical evidence of bubbles for some other events we also compare the ds lppls method to the exponential curve fitting and the generalized sup adf test approaches and find that ds lppls system is more accurate in identifying well known bubble events with significantly smaller numbers of false negatives and false positives

a harmonic analysis approach to essential normality of principal submodules guo and the second author have shown that the closure i in the drury arveson space of a homogeneous principal ideal i in c z1 zn is essentially normal in this note the authors extend this result to the closure of any principal polynomial ideal in the bergman space in particular the commutators and cross commutators of the restrictions of the multiplication operators are shown to be in the schatten p class for p n the same is true for modules generated by polynomials with vector valued coefficients further the maximal ideal space xi of the resulting c algebra for the quotient module is shown to be contained in z i bn where z i is the zero variety for i and to contain all points in bn that are limit points of z i bn finally the techniques introduced enable one to study a certain class of weight bergman spaces on the ball

a hierarchical model of financial crashes abstract we follow up our previous conjecture that large stock market crashes are analogous to critical points in statistical physics the term critical refers to regimes of cooperative behavior such as magnetism at the curie temperature and liquid gas transitions and is characterized by the singular mathematical behavior of relevant observables to illustrate the concept of criticality we present a simple hierarchical model of traders exhibiting crowd behavior and show that it has a well defined critical point whose mathematical signature is a power law dependence of the price modulated by log periodic structures as recently found in market data by several independent groups

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

geometric representation theory for unitary groups of operator algebras geometric realizations for the restrictions of gns representations to unitary groups of c algebras are constructed these geometric realizations use an appropriate concept of reproducing kernels on vector bundles to build such realizations in spaces of holomorphic sections a class of complex coadjoint orbits of the corresponding real banach lie groups are described and some homogeneous holomorphic hermitian vector bundles that are naturally associated with the coadjoint orbits are constructed

models for noncommuting operators abstract this paper develops a model theory for a pair of noncommuting operators using backward shift operators on a fock space rota s theorem is generalized i e it is shown that any two bounded operators on a hilbert space are simultaneously similar to part of a pair of backward shift operators on a fock space these shift operators and the fock space framework are also used to develop a dilation theory for two noncommuting operators

an index theory for quantum dynamical semigroups w arveson showed a way of associating continuous tensor product systems of hilbert spaces with endomorphism semigroups of type i factors we do the same for general quantum dynamical semigroups through a dilation procedure the product system so obtained is the index and its dimension is a numerical invariant for the original semigroup

dilations wandering subspaces and inner functions the objective of this paper is to study wandering subspaces for commuting tuples of bounded operators on hilbert spaces it is shown that for a large class of analytic functional hilbert spaces h k on the unit ball in c n wandering subspaces for restrictions of the multiplication tuple m z m z1 m zn can be described in terms of suitable h k inner functions we prove that h k inner functions are contractive multipliers and deduce a result on the multiplier norm of quasi homogeneous polynomials as an application along the way we prove a refinement of a result of arveson on the uniqueness of minimal dilations of pure row contractions c 2017 elsevier inc all rights reserved

fractal structure of zeros in hierarchical models we consider an ising and aq state potts model on a diamond hierarchical lattice we give pictures of the distribution of zeros of the partition function in the complex plane of temperatures for several choices ofq these zeros are just the julia set corresponding to the renormalization group transformation

free biholomorphic functions and operator model theory ii let f f1 fn be an n tuple of formal power series in noncommutative indeterminates z1 zn such that f 0 0 and the jacobian detjf 0 0 and let g g1 gn be its inverse with respect to composition we assume that f and g have nonzero radius of convergence and g is a bounded free holomorphic function on the open unit ball b h n 1 where b h is the algebra of bounded linear operators an a hilbert space h in this paper several results concerning the noncommutative multivariable operator theory on the unit ball b h n 1 are extended to the noncommutative domain bf h x b h n g f x x and f x 1 for an appropriate evaluation x f x we develop an operator model theory and dilation theory for bf h where the associated universal model is an n tuple mz1 mzn of left multiplication operators acting on a hilbert space h2 f of formal power series all the results of this paper have commutative versions

the dirac operator of a commuting d tuple abstract given a commuting d tuple t t1 td of otherwise arbitrary operators on a hilbert space there is an associated dirac operator dt significant attributes of the d tuple are best expressed in terms of dt including the taylor spectrum and the notion of fredholmness in fact all properties of t derive from its dirac operator we introduce a general notion of dirac operator in dimension d 1 2 that is appropriate for multivariable operator theory we show that every abstract dirac operator is associated with a commuting d tuple and that two dirac operators are isomorphic iff their associated operator d tuples are unitarily equivalent by relating the curvature invariant introduced in a previous paper to the index of a dirac operator we establish a stability result for the curvature invariant for pure d contractions of finite rank it is shown that for the subcategory of all such t that are a fredholm and and b graded the curvature invariant k t is stable under compact perturbations we do not know if this stability persists when t is fredholm but ungraded although there is concrete evidence that it does

multiplier algebras of complete nevanlinna pick spaces dilations boundary representations and hyperrigidity abstract we study reproducing kernel hilbert spaces on the unit ball with the complete nevanlinna pick property through the representation theory of their algebras of multipliers we give a complete description of the representations in terms of the reproducing kernels while representations always dilate to representations of the ambient c algebra we show that in our setting we automatically obtain coextensions in fact we show that in many cases this phenomenon characterizes the complete nevanlinna pick property we also deduce operator theoretic dilation results which are in the spirit of work of agler and several other authors moreover we identify all boundary representations compute the c envelopes and determine hyperrigidity for certain analogues of the disc algebra finally we extend these results to spaces of functions on homogeneous subvarieties of the ball

spherical contractions and interpolation problems on the unit ball in this note fractional representations of multipliers on vector valued functional hilbert spaces are used to give a proof of arveson s version of von neumann s inequality for n contractions on the unit ball we prove a commutant lifting theorem for operators on the classical hardy space over the unit ball in mathbb c n as applications we obtain interpolation results for functions in the schur class we deduce a toeplitz corona theorem on the unit ball and we give a simplified definition of arveson s curvature invariant for n contractions with finite dimensional defect space in the final part we describe a solution of the operator valued nevanlinna pick problem with uniform bounds on uniqueness sets in the unit ball

a stable and robust calibration scheme of the log periodic power law model abstract we present a simple transformation of the formulation of the log periodic power law formula of the johansen ledoit sornette jls model of financial bubbles that reduces it to a function of only three nonlinear parameters the transformation significantly decreases the complexity of the fitting procedure and improves its stability tremendously because the modified cost function is now characterized by good smooth properties with in general a single minimum in the case where the model is appropriate to the empirical data we complement the approach with an additional subordination procedure that slaves two of the nonlinear parameters to the most crucial nonlinear parameter the critical time t c defined in the jls model as the end of the bubble and the most probable time for a crash to occur this further decreases the complexity of the search and provides an intuitive representation of the results of the calibration with our proposed methodology metaheuristic searches are not longer necessary and one can resort solely to rigorous controlled local search algorithms leading to a dramatic increase in efficiency empirical tests on the shanghai composite index sse from january 2007 to march 2008 illustrate our findings

bergman inner functions and m hypercontractions abstract we characterize operator valued bergman inner functions on the unit ball as functions admitting a suitable transfer function realization thus we extend corresponding one variable results of olofsson from the case of the unit disc to the unit ball at the same time we associate with each m hypercontraction t l h n a canonical bergman inner function w t and indicate a possible definition of a characteristic function t for t

gleason s problem and schur multipliers in the multivariable quaternionic setting abstract we define and study the counterparts of gleason s problem of the drury arveson s space and of schur multipliers when the unit ball of c n is replaced by the unit ball of h n where h denotes the algebra of real quaternions schur multipliers are characterized in terms of coisometric operator matrices in quaternionic spaces finally we define the counterpart of blaschke factors in this setting and study a one point interpolation problem

characteristic function for polynomially contractive commuting tuples abstract in this note we develop the theory of characteristic function as an invariant for n tuples of operators the operator tuple has a certain contractivity condition put on it this condition and the class of domains in c n that we consider are intimately related a typical example of such a domain is the open euclidean unit ball given a polynomial p in c z 1 z 2 z n whose constant term is zero all the coefficients are nonnegative and the coefficients of the linear terms are nonzero one can naturally associate a reinhardt domain with it which we call the p ball definition 1 1 using the reproducing kernel hilbert space h p c associated with this reinhardt domain in c n s pott constructed the dilation for a polynomially contractive commuting tuple definition 1 2 s pott standard models under polynomial positivity conditions j operator theory 41 1999 365 389 mr 2000j 47019 given any polynomially contractive commuting tuple t we define its characteristic function t which is a multiplier we construct a functional model using the characteristic function exploiting the model we show that the characteristic function is a complete unitary invariant when the tuple is pure the characteristic function gives newer and simpler proofs of a couple of known results one of them is the invariance of the curvature invariant and the other is a beurling theorem for the canonical operator tuple on h p c it is natural to study the boundary behaviour of t in the case when the domain is the euclidean unit ball we do that and here essential differences with the single operator situation are brought out

dilations and commutant lifting for jointly isometric operators a geometric approach abstract a tuple of commuting contractions t t 1 t 2 t n is called a joint isometry if t j t j i we give a geometric proof that joint isometries have a regular unitary dilation and that its commutant lifts we also show that t is subnormal and that its minimal normal extension is also jointly isometric

cyclic row contractions and rigidity of invariant subspaces abstract it is known that pure row contractions with one dimensional defect spaces can be classified up to unitary equivalence by compressions of the standard d shift acting on the full fock space upon settling for a softer relation than unitary equivalence we relax the defect condition and simply require the row contraction to admit a cyclic vector we show that cyclic pure row contractions can be transformed in a precise technical sense into compressions of the standard d shift cyclic decompositions of the underlying hilbert spaces are the natural tool to extend this fact to higher multiplicities we show that such decompositions face multivariate obstacles of an algebraic nature nevertheless decompositions are obtained for nilpotent commuting row contractions by analyzing function theoretic rigidity properties of their invariant subspaces

multivariable bohr inequalities operator valued multivariable bohr type inequalities are obtained for i a class of noncommutative holomorphic functions on the open unit ball of generalizing the analytic functions on the open unit disc ii the noncommutative disc algebra and the noncommutative analytic toeplitz algebra iii a class of noncommutative selfadjoint harmonic functions on the open unit ball of generalizing the real valued harmonic functions on the open unit disc iv the cuntz toeplitz algebra the reduced resp full group algebra resp of the free group with generators v a class of analytic functions on the open unit ball of the classical bohr inequality is shown to be a consequence of fejer s inequality for the coefficients of positive trigonometric polynomials and haager up de la harpe inequality for nilpotent operators moreover we provide an inequality which for analytic polynomials on the open unit disc is sharper than bohr s inequality

invariant subspaces and operator model theory on noncommutative varieties let mathcal q subset mathbb c left be an arbitrary set of polynomials in noncommutative indeterminates such that q 0 0 for all q in mathcal q the noncommutative variety begin aligned mathcal v f mathcal q m mathcal h left x x 1 ldots x n in mathbf d f m mathcal h q x 0 text for all q in mathcal q right end aligned where mathbf d f m mathcal h is a noncommutative regular domain in b mathcal h n and b mathcal h is the algebra of bounded linear operators on a hilbert space mathcal h admits a universal model b m b 1 m ldots b n m such that q b m 0 q in mathcal q acting on a model space which is a subspace of the full fock space with n generators in this paper we obtain a beurling type characterization of the joint invariant subspaces under the operators b 1 m ldots b n m in terms of partially isometric multi analytic operators acting on model spaces more generaly a beurling lax halmos type representation is obtained and used to parameterize the wandering subspaces of the joint invariant subspaces under b 1 m otimes i mathcal e ldots b n m otimes i mathcal e and to characterize when they are generating for the corresponding invariant subspaces similar results are obtained for any pure n tuple x 1 ldots x n in the noncommutative variety mathcal v f mathcal q m mathcal h we characterize the elements in the noncommutative variety mathcal v f mathcal q m mathcal h which admit characteristic functions develop an operator model theory for the completely non coisometric elements and prove that the characteristic function is a complete unitary invariant for this class of elements this extends the classical sz nagy foias functional model for completely non unitary contractions based on characteristic functions our results apply in particular when mathcal q consists of the noncommutative polynomials z iz j z jz i i j 1 ldots n in this case the model space is a symmetric weighted fock space which is identified with a reproducing kernel hilbert space of holomorphic functions on a reinhardt domain in mathbb c n and the universal model is the n tuple m lambda 1 ldots m lambda n of multipliers by the coordinate functions

toeplitz operators associated to commuting row contractions let h be a complex hilbert space and let tn n 1 be a sequence of commuting bounded operators on h such that n 1tntn ih let f t denote the space of all operators x in b h for which n 1tnxtn x and suppose that f t 0 we will show that there exists a triple k un n 1 where k is a hilbert space k h is a bounded operator and un n 1 b k is a sequence of commuting normal operators with n 1unun ik such that tn un for n 1 and for which the mapping y y is a complete isometry from the commutant of un n 1 onto the space f t moreover we show that the inverse of this mapping can be extended to a homomorphism c ih f t un n 1 from the unital c algebra generated by f t onto the commutant of un n 1 we also show that there exists a homomorphism c ih tn n 1 c ik un n 1 such that tn un for n 1 in the particular case when tn n 1 has only a finite number of non zero components it turns out that un n 1 is unitarily equivalent to the spherical unitary part of the standard commuting dilation of tn n 1

an operator valued poisson kernel abstract versions of the cauchy and poisson formulas in the unit ball of c n are defined by means of appropriate operator valued kernels connections with some problems of dilation theory are then made

residually finite dimensional operator algebras abstract we study non selfadjoint operator algebras that can be entirely understood via their finite dimensional representations in contrast with the elementary matricial description of finite dimensional c algebras in the non selfadjoint setting we show that an additional level of flexibility must be allowed motivated by this peculiarity we consider a natural non selfadjoint notion of residual finite dimensionality we identify sufficient conditions for the tensor algebra of a c correspondence to enjoy this property to clarify the connection with the usual self adjoint notion we investigate the residual finite dimensionality of the minimal and maximal c covers associated to an operator algebra

on a bitangential interpolation problem for contractive valued functions on the unit ball we solve the bitangential interpolation problem with a finite number of interpolation nodes for a multivariable analogue of the schur class consisting of matrix valued analytic functions on the ball the interpolation conditions are formulated via a generalized functional calculus with operator argument thereby generalizing in a compact way the simple first order interpolation conditions considered for this class of functions in earlier work the description of all solutions is given via a redheffer transform whose entries are given explicitly in terms of the interpolation data

carleson measures for besov spaces on the ball with applications abstract carleson and vanishing carleson measures for besov spaces on the unit ball of c n are characterized in terms of berezin transforms and bergman metric balls the measures are defined via natural imbeddings of besov spaces into lebesgue classes by certain combinations of radial derivatives membership in schatten classes of the imbeddings is considered too some carleson measures are not finite but the results extend and provide new insight to those known for weighted bergman spaces special cases pertain to arveson and dirichlet spaces and a unified view with the usual hardy space carleson measures is presented by letting the order of the radial derivatives tend to 0 weak convergence in besov spaces is also characterized and weakly 0 convergent families are exhibited applications are given to separated sequences operators of forelli rudin type gap series characterizations of weighted bloch lipschitz and growth spaces inequalities of fejer riesz and hardy littlewood type and integration operators of cesaro type

renormalization group analysis of the 2000 2002 anti bubble in the us s p500 index explanation of the hierarchy of five crashes and prediction abstract we propose a straightforward extension of our previously proposed log periodic power law model of the anti bubble regime of the usa stock market since the summer of 2000 in terms of the renormalization group framework to model critical points using a previous work by gluzman and sornette phys rev e 65 2003 036142 on the classification of the class of weierstrass like functions we show that the five crashes that occurred since august 2000 can be accurately modeled by this approach in a fully consistent way with no additional parameters our theory suggests an overall consistent organization of the investors forming a collective network which interact to form the pessimistic bearish anti bubble regime with intermittent acceleration of the positive feedbacks of pessimistic sentiment leading to these crashes we develop retrospective predictions that confirm the existence of significant arbitrage opportunities for a trader using our model finally we offer a prediction for the unknown future of the us s p500 index extending over 2003 and 2004 that refines the previous prediction of sornette and zhou quant finance 2 2002 468

a boundary nevanlinna pick problem for a class of analytic matrix valued functions in the unit ball abstract we solve a tangential boundary interpolation problem with a finite number of interpolating points for a multivariable analogue of the schur class the description of all solutions is parametrized in terms of a linear fractional transformation whose entries are given explicitly in terms of the interpolation data

poisson transforms on some c algebras generated by isometries abstract a noncommutative poisson transform associated to a certain class of sequences of operators on hilbert spaces with property p is defined on some universal c algebras resp nonselfadjoint algebras generated by isometries its properties are described and used to study these universal algebras and their representations as consequences we obtain a functional calculus isometric resp unitary dilations and commutant lifting theorem for the class of sequences of operators with property p our geometrical approach leads also to new and elementary proofs as well as extensions of some classical results

completely induced fuzzy topological spaces abstract the object of this paper is to introduce and to study the concepts of completely induced fuzzy topological spaces and completely lower semi continuous functions completely lower semi continuous functions turn out to be the natural tool for studying the completely induced fuzzy topological spaces

berezin transforms on noncommutative varieties in polydomains abstract let q be a set of polynomials in noncommutative indeterminates z i j i 1 k j 1 n i in this paper we study noncommutative varieties v q h x x i j d h g x 0 for all g q where d h is a regular polydomain in b h n 1 n k and b h is the algebra of bounded linear operators on a hilbert space h under natural conditions on q we show that there is a universal model s s i j such that g s 0 g q acting on a subspace of a tensor product of full fock spaces we characterize the variety v q h and its pure part in terms of the universal model and a class of completely positive linear maps we obtain a characterization of those elements in v q h which admit characteristic functions and prove that the characteristic function is a complete unitary invariant for the class of completely non coisometric elements we study the universal model s its joint invariant subspaces and the representations of the universal operator algebras it generates the variety algebra a v q the hardy algebra f v q and the c algebra c v q using noncommutative berezin transforms associated with each variety we develop an operator model theory and dilation theory for large classes of varieties in noncommutative polydomains this includes various commutative cases which are closely connected to the theory of holomorphic functions in several complex variables and algebraic geometry

fuzzy topological spaces we start by discussing a class of special fuzzy topological spaces that is the product induced spaces s first we show that every fuzzy topological space is topologically isomorphic with a certain topological space and then proceed to prove every open fuzzy set is defined by some lower semicontinuous function taking this as the background we introduce the concept of dual points 6 and thus establish a kind of neighborhood structure of fuzzy points such that the q neighborhood 4 which is one of the important notions in fuzzy topology and the neighborhood arc integrated in this structure this neighborhood structure will be the core of our developing the theory of fuzzy topological spaces we introduce the concept of strong quasi discoincident 1 i and so give a group of fuzzy separation properties which is a most natural generalization of the usual separation properties next we introduce a kind of fuzzy metrics and use this metrics directly to discuss the fuzzy metric space by means of fuzzy points wc define kinds of uniformities discuss their fundamental properties and extend weil s theorem on usual topology to fuzzy topological spaces and hence obtain their separation character naturally these fuzzy uniformities can still be characterized by a family of fuzzy metrics finally we discuss the problem of fuzzy mctrization on fuzzy topological spaces and obtain a fuzzy metrization theorem which contains the nagata smirnov theorem as a special example