vector arma estimation a reliable subspace approach a parameter estimation method for finite dimensional multivariate linear stochastic systems which is guaranteed to produce valid models approximating the true underlying system in a computational time of a polynomial order in the system dimension is presented this is achieved by combining the main features of certain stochastic subspace identification techniques with sound matrix schur restabilizing procedures and multivariate covariance fitting both of which are formulated as linear matrix inequality problems all aspects of the identification method are discussed with an emphasis on the two issues mentioned above and examples of the overall performance are provided for two different systems

on restricted perturbations in inverse images and a description of normalizer algebras in c algebras abstract let e and f be banach spaces and t a bounded linear map from e into f using a certain perturbation function t we find a useful sufficient criterion that t maps the closed unit ball onto a closed set applying this to the quotient map from a c algebra a onto its quotient banach space a l r by the sum l r of closed left and right ideals l and r of a we obtain that the closed unit ball of a maps onto the closed unit ball of a l r this gives an independent description of the images of the right normalizer algebra n r d and the normalizer algebra n d n l d n r d of a hereditary c subalgebra d of a by the quotient map from a onto a cl ad cl da we use this to prove a necessary and sufficient criterion for a c algebra b to be a c quotient algebra of a c subalgebra of a c algebra a the latter criterion will be applied in the situation where a equals the car algebra in some forthcoming papers cf section 6 for more details

factorization in analytic operator algebras abstract a constructive and unified approach is used to obtain the upper lower factorization of positive operators and the outer function factorization of positive operator valued functions on the circle for a projection nest e it is shown that every positive operator admits a canonical factorization c a a with a an outer operator if and only if e is well ordered with new methods we generalize the inner outer factorizations obtained by arveson for nests of order type z and the riesz factorization due to shields for trace class triangular operators weak factorization is obtained in noncommutative h1 spaces associated with general nest subalgebras of a semifinite factor characterizations of a nehari type are given for the associated hankel forms and hankel operators

on normal subgroups of multiplicative group of skew fields generated by a polycyclic by finite group 1 1 let d be a field and let d be its multiplicative group consider a subgroup g c d and a subring k of the center of d we denote the subfield the term field in this paper is used in the skew field sense generated by k and g by k g when k is the subring generated by the unit elements i e k z or k z we simply say that d is generated by g the main result of the article is the following theorem

une minoration de la norme de l operateur de cauchy sur les graphes lipschitziens it was shown by t murai that the norm of the operator defined by the cauchy kernel on the graph of a lipschitz function a is less than c 1 iiatlioo l 2 we use garnett s example to show that this estimate is optimal

dimensions and singular traces for spectral triples with applications to fractals given a spectral triple a h d the functionals on a of the form a a d are studied where is a singular trace and is a generalised limit when is the dixmier trace the unique exponent d giving rise possibly to a non trivial functional is called hausdorff dimension and the corresponding functional the d dimensional hausdorff functional it is shown that the hausdorff dimension d coincides with the abscissa of convergence of the zeta function of d 1 and that the set of s for which there exists a singular trace giving rise to a non trivial functional is an interval containing d moreover the endpoints of such traceability interval have a dimensional interpretation the functionals corresponding to points in the traceability interval are called hausdorff besicovitch functionals these definitions are tested on fractals in r by computing the mentioned quantities and showing in many cases their correspondence with classical objects in particular for self similar fractals the traceability interval consists only of the hausdorff dimension and the corresponding hausdorff besicovitch functional gives rise to the hausdorff measure more generally for any limit fractal the described functionals do not depend on the generalized limit

trace class operators and commutators abstract we identify the linear span of commutators ab ba where a is a trace class operator and b is any bounded operator on a separable hilbert space or where a b are both hilbert schmidt operators thus answering questions raised by work of anderson vaserstein and weiss

weak limits of projections and compactness of subspace lattices a strongly closed lattice of projections on a hilbert space is compact if the associated algebra of operators has a weakly dense subset of compact operators if the lattice is commutative there are necessary and sufficient conditions for compactness one in terms of the structure of the lattice and the other in terms of a measure on the lattice there are many examples of compact lattices and two main types of examples of noncompact lattices compactness is also re ated to the study of weak limits of certain projections in a3 arveson generalized n andersen s important theorem on continuous nests an theorem 3 5 5 to certain commutative subspace lattices associated with e continuous measures an important property of these lattices is that they are compact in the strong operator topology since compactness is also a property of nests and plays an important role in the similarity theory for nests da2 la an we investigate in this paper the problem of determining which subspace lattices are compact a greater understanding of this problem will hopefully help in the development of similarity theory for other lattices it should be noted that it is well known that there are also noncompact lattices namely orthocomplemented commutative subspace lattices in 2 we give a main result theorem 2 2 which provides a connection between compactness of a lattice s and the presence of compact operators in the associated operator algebra alg s this result provides many examples of compact lattices it also shows that there is a relationship between complete distributivity compactness and other nice properties especially if the lattice is commutative 3 deals with properties of noncompact lattices included are two conditions equivalent to noncompactness for commutative lattices one is essentially measuretheoretic and the other is a condition on the structure of the lattice we also give two quite different classes of examples of noncompact lattices in the process we obtain a representation theorem for certain infinite tensor products of commutative subspace lattices which extends a result in ghl we then show that most infinite tensor products are noncompact one simple condition determining compactness is whether or not the lattice has any nonprojection weak limits proposition 2 1 this property is related to a paper received by the editors june 27 1986 some of the results in this paper were presented at the nsf cbms conference on quasitriangularity and analyticity in operator algebras texas tech university august 1 1983 1980 mclthemcltics subject clussificcltion 1985 revision primary 47d25 1987 american mathematical society 0002 9947 87 1 00 25 per page 515 this content downloaded from 207 46 13 176 on mon 20 jun 2016 06 42 17 utc all use subject to http about jstor org terms

entropy of some automorphisms of the ii 1 factor of the free group in infinite number of generators letl f be theii 1 factor defined by the free groupf in infinite number of generators it is shown that for a class of automorphisms ofl f arising from bijections of the set of generators off on itself and including the free shift the entropy is zero

s numbers of singular integrals for the invariance of absolutely continuous spectra in fractional dimensions an important consequence of the kato rosenblum theorem in abstract scattering theory 5 81 is the invariance up to unitary equivalence of absolutely continuous spectra under trace class perturbations the extension of this fact to higher integral dimensions was given in lo a careful inspection of trace class scattering theory reveals the crucial role of l2 boundedness of the hilbert transform in the one dimensional case in the n dimensional generalization this is replaced by the asymptotics of fourier coefficients of 2 1 x k c n 1 11 2 on the torus or equivalently by the asymptotics of s numbers of corresponding singular integrals the general functional analysis machinery developed in 9 lo for studying normed ideal perturbations of systems of hilbert space operators reduces this kind of operator theory questions to questions about the existence or non existence of quasicentral approximate units relative to normed ideals the existence of quasicentral approximate units in turn is related to commutator questions 11 j for related considerations in the quasidiagonality context see 7 the natural operators to examine are then singular integral operators in this paper we consider the fractional dimensional case the natural singular integral problem in this case is to estimate the s numbers of singular integrals with kernels yjl lx 1 in l p where 1 is a compactly supported probability measure on w of fractional dimension like hausdorff measure restricted to suitable compacta the results we

dynamical entropy of c algebras and von neumann algebras the definition of the dynamical entropy is extended for automorphism groups ofc algebras as an example the dynamical entropy of the shift of a lattice algebra is studied and it is shown that in some cases it coincides with the entropy density

the problem of deficiency indices for discrete schrodinger operators on locally finite graphs the number of self adjoint extensions of a symmetric operator acting on a complex hilbert space is characterized by its deficiency indices given a locally finite unoriented simple tree we prove that the deficiency indices of any discrete schrodinger operator are either null or infinite we also prove that all deterministic discrete schrodinger operators which act on a random tree are almost surely self adjoint furthermore we provide several criteria of essential self adjointness we also address some importance to the case of the adjacency matrix and conjecture that given a locally finite unoriented simple graph its deficiency indices are either null or infinite besides that we consider some generalizations of trees and weighted graphs

nearly weakly orthonormal sequences singular value estimates and calderon zygmund operators abstract the direct way to estimate the singular values of a compact operator is to decompose it as a sum of orthogonal rank one pieces however such decompositions can generally not be found in practice we give a variation of the decomposition using nearly weakly orthonormal nwo sequences the nwo decomposition is easier to do in examples but is still strong enough to give good singular value estimates we illustrate this by giving sharp trace ideal estimates for the double layer potential and for the first and higher commutators of multiplication operators and calderon zygmund operators in particular nwo sequences seem well suited for dealing with operators which depend nonlinearly on their symbol we also show that the class of operators which admit nwo expansions is well behaved under composition under conjugation by weights and under conjugation by changes of variable

which traces are spectral abstract among ideals of compact operators on a hilbert space we identify a subclass of those closed with respect to the logarithmic submajorization within this subclass we answer the questions asked by pietsch 22 and by dykema figiel weiss and wodzicki 7 in the first case we show that lidskii type formulae hold for every trace on such ideal in the second case we provide the description of the commutator subspace associated with a given ideal finally we prove that a positive trace on an arbitrary ideal is spectral if and only if it is monotone with respect to the logarithmic submajorization

the bott borel weil theorem for direct limit groups we show how highest weight representations of certain infinite dimensional lie groups can be realized on cohomology spaces of holomorphic vector bundles this extends the classical bott borel weil theorem for finite dimensional compact and complex lie groups our approach is geometric in nature in the spirit of bott s original generalization of the borel weil theorem the groups for which we prove this theorem are strict direct limits of compact lie groups or their complexifications we previously proved that such groups have an analytic structure our result applies to most of the familiar examples of direct limits of classical groups we also introduce new examples involving iterated embeddings of the classical groups and see exactly how our results hold in those cases one of the technical problems here is that in general the limit lie algebras will have root systems but need not have root spaces so we need to develop machinery to handle this somewhat delicate situation

group presentation p adic analytic groups and lattices in mathrm sl _2 mathbf c groups by using their pro p completions this method is based on the observation that if x r is a presentation of the finitely generated f g group f then x r considered as a presentation for a pro p group is actually a presentation for t the pro p completion of f first we prove a generalization of a theorem of golod and shafarevich cf h theorem let g be a p adic analytic pro p group different from zp the p adic integers if x r is a minimal presentation of g then 1x 2 iri 2

folner conditions nuclearity and subexponential growth inc algebras answering a first question of voiculescu on the existence of quasi central approximate units relative to normed ideals j funct anal 91 1990 1 36 vaillant 8 and kirchberg onc algebras having subexponential polynomial and linear growth invent math 108 1992 635 652 showed that subexponential growth implies nuclearity in thec context voiculescu suggested a folner type condition forc algebras and asked about the relation to growth and nuclearity in this work we clarify the relation among subexponential growth phenomena this folner condition suggested by voiculescu weak filtrability in the sense of arveson and bedos and nuclearity in thec algebra context

q positive definiteness and related operators abstract we are in progress of extending the family of q deformed operators considered in the previous papers by joining to them q subnormal as well as q formally subnormal ones it turns out that q positive definiteness a notion generalizing halmos standard positive definiteness of bounded subnormal operators is likewise central for our new scheme

fubini theorem in noncommutative geometry abstract we discuss the fubini formula in alain connes noncommutative geometry we present a sufficient condition on spectral triples for which a fubini formula holds true the condition is natural and related to heat semigroup asymptotics we provide examples of spectral triples for which the fubini formula fails

optimal linear identifying codes identifying codes can be used to locate malfunctioning processors we say that a code c of length n is a linear 1 spl les l identifying code if it is a subspace of f sub 2 sup n and for all x y spl sube f sub 2 sup n such that x y spl les l and x spl ne y we have spl cup sub x spl isin x b x spl cap c spl ne spl cup y spl isin y b y spl cap c strongly 1 spl les l identifying codes are a variant of identifying codes we determine the cardinalities of optimal linear 1 spl les l identifying and strongly 1 spl les l identifying codes in hamming spaces of any dimension for locating any at most l malfunctioning processors

an infinite dimensional schur horn theorem and majorization theory the main result of this paper is the extension of the schur horn theorem to infinite sequences for two nonincreasing nonsummable sequences and that converge to 0 there exists a positive compact operator a with eigenvalue list and diagonal sequence if and only if j 1n j j 1n j for every n if and only if q for some orthostochastic matrix q when and are summable requiring additionally equality of their infinite series obtains the same conclusion extending a theorem by arveson and kadison our proof depends on the construction and analysis of an infinite product of t transform matrices

a generalization of voiculescu s theorem for normal operators to semifinite von neumann algebras abstract in this paper we provide a generalized version of voiculescu s theorem for normal operators by showing that in a von neumann algebra with separable pre dual and a faithful normal semifinite tracial weight each normal operator is an arbitrarily small max 2 norm perturbation of a diagonal operator furthermore in a countably decomposable properly infinite von neumann algebra with a faithful normal semifinite tracial weight we prove that each self adjoint operator can be diagonalized modulo normed ideals satisfying a natural condition an analogue for nuclear c algebras of voiculescu s absorption theorem 33 theorem 2 4 is also proved in the case of semifinite factors

on c algebras having linear polynomial and subexponential growth answering a question of voiculescu 16 problem 5 9 we show thatc algebras having filtrations an n satisfying the condition lim supn ln diman n 0 in particular having subexponential growth are nuclear

a condition for diagonalization modulo arbitrary norm ideals abstract we give a spectral condition which is sufficient for the simultaneous diagonalization of a commuting tuple of self adjoint operators modulo a given norm ideal for diagonalization modulo certain norm ideals this condition is also necessary while for other norm ideals this condition seems to be close to being necessary moreover this condition is easy to verify in applications

traces of compact operators and the noncommutative residue abstract we extend the noncommutative residue of m wodzicki on compactly supported classical pseudo differential operators of order d and generalise a connes trace theorem which states that the residue can be calculated using a singular trace on compact operators contrary to the role of the noncommutative residue for the classical pseudo differential operators a corollary is that the pseudo differential operators of order d do not have a unique trace pseudo differential operators can be non measurable in connes sense other corollaries are given clarifying the role of dixmier traces in noncommutative geometry including the definitive statement of connes original theorem

diagonalization modulo a class of orlicz ideals abstract we consider a class of norm ideals c g which are non commutative analogues of orlicz spaces and which satisfy a previously introduced condition called qk we give a spectral condition which is necessary and sufficient for a commuting tuple of self adjoint operators a a 1 a n to be simultaneously diagonalizable modulo c g

amenable unitary representations of locally compact groups a notion of amenability for an arbitrary unitary group representation is introduced this unifies and generalizes the notions of amenable homogeneous spaces and of inner amenable groups amenable locally compact groups are characterized by the amenability of all their unitary representations amenable representations are characterized by several properties which are operator theoretic analogues of properties characterizing amenable groups we give a generalization to arbitrary representations of hulanicki reiter theorem this is used in order to describe the amenable representations of the groups with kazhdan property t

compact operators invariant subspaces and spectral synthesis let l be a subspace lattice which contains a sequence pn of commuting projections such that for any subsequence pni vpni i and pni 0 then alg l k h 0 suppose g is a compact abelian group and e g is a closed set there is a family le of commutative subspace lattices for which alg le k h 0 precisely when e is a set of multiplicity in the sense of harmonic analysis by showing that the graph of is a set of uniqueness in 2 2 we obtain a thin set proof that alg 2 m12 contains no nonzero compact operators for an important class of sets k g gamin k amax k iff k is a set of spectral synthesis in the group g x g it follows that if e1and e2 are sets of spectral synthesis in g then alg pe1 bo alg pe2 alg pe1 pe2iff e1 e2 is a set of spectral synthesis in g x g and if semigroups 1 and 2 are sets of spectral synthesis in g then alg 1 bo alg 2 alg 1 2iff 1 2 is a set of spectral synthesis in g g the operator algebra alg p1 p2 is synthetic iff for all n alg p1 pn is synthetic this implies that the operator algebras alg 2 mp are synthetic

perturbation theory for groups and lattices abstract a generalization of a theorem of dan voiculescu on perturbations of separable c algebras is proved this is applied to solve two problems relating to the perturbation theory of unitary group representations and of commutative subspace lattices the latter generalizes a theorem of niels toft andersen on compact perturbations of nests

crossed products of operator algebras applications of takai duality abstract let g be a partially ordered abelian group with haar measure let a g be a dynamical system and let a be the associated semicrossed product using takai duality we establish a stable isomorphism a s a k g ad g where k g denotes the compact operators in the csl algebra alg l g and denotes the right regular representation of g we also show that there exists a complete lattice isomorphism between the invariant ideals of a and the ad invariant ideals of a k g using takai duality we also continue our study of the radical for the crossed product of an operator algebra and we solve open problems stemming from the earlier work of the authors among others we show that the crossed product of a radical operator algebra by a compact abelian group is a radical operator algebra we also show that the permanence of semisimplicity fails for crossed products by r a final section of the paper is devoted to the study of radically tight dynamical systems i e dynamical systems a g for which the identity rad a g rad a g persists a broad class of such dynamical systems is identified

free subalgebras of c algebras abstract the aim of this work is to study the existence of free subalgebras in c algebras the kurosh levitzky problem and related conjectures of makar limanov are answered in the context of c algebras in particular we characterize and study the existence of free non abelian subalgebras with two self adjoint contractions in finitely generated c algebras c algebras having linear growth are shown to be subhomogeneous

least squares approximation of fir by iir digital filters an algorithm is presented for the least squares approximation of fir filters by iir filters the algorithm is an iterative procedure where each iteration requires the solution of an overdetermined set of linear equations and some digital filtering operations all calculations are performed with the numerator and denominator coefficients of the transfer functions a conversion to state space descriptions is not necessary examples show that the approximation error is as small as that of the iir filters obtained with balanced model reduction moreover the effects of numerical errors are negligible thus our algorithm is applicable even in cases where the fir filter length is large

combining evolutionary and stochastic gradient techniques for system identification in the present contribution a novel method combining evolutionary and stochastic gradient techniques for system identification is presented the method attempts to solve the autoregressive moving average arma system identification problem using a hybrid evolutionary algorithm which combines genetic algorithms gas and the least mean squares lms algorithm more precisely lms is used in the step of the evaluation of the fitness function in order to enhance the chromosomes produced by the ga experimental results demonstrate that the proposed method manages to identify unknown systems even in cases with high additive noise furthermore it is observed that in most cases the proposed method finds the correct order of the unknown system without using a lot of a priori information compared to other system identification methods presented in the literature so the proposed hybrid evolutionary algorithm builds models that not only have small mse but also are very similar to the real systems except for that all models derived from the proposed algorithm are stable

iwasawa decompositions of some infinite dimensional lie groups we set up an abstract framework that allows the investigation of iwasawa decompositions for involutive infinite dimensional lie groups modeled on banach spaces this provides a method to construct iwasawa decompositions for classical real or complex banach lie groups associated with the schatten ideals o p h on a complex separable hilbert space h if 1 p

diagonalization modulo norm ideals with lipschitz estimates abstract suppose that x d is a compact metric space and that is a regular borel measure on x let lip x denote the collection of lipschitz functions on x in this paper we investigate the problem of simultaneous diagonalization of the multiplication operators m f f lip x on l 2 x modulo norm ideals of compact operators

on determining the domain of the adjoint operator abstract a theorem that is of aid in computing the domain of the adjoint operator is provided it may serve e g as a criterion for selfadjointness of a symmetric operator for normality of a formally normal operator or for h selfadjointness of an h symmetric operator differential operators and operators given by an infinite matrix are considered as examples

on a new class of codes for identifying vertices in graphs we investigate a new class of codes for the optimal covering of vertices in an undirected graph g such that any vertex in g can be uniquely identified by examining the vertices that cover it we define a ball of radius t centered on a vertex spl upsi to be the set of vertices in g that are at distance at most t from spl upsi the vertex spl upsi is then said to cover itself and every other vertex in the ball with center spl upsi our formal problem statement is as follows given an undirected graph g and an integer t spl ges 1 find a minimal set c of vertices such that every vertex in g belongs to a unique set of balls of radius t centered at the vertices in c the set of vertices thus obtained constitutes a code for vertex identification we first develop topology independent bounds on the size of c we then develop methods for constructing c for several specific topologies such as binary cubes nonbinary cubes and trees we also describe the identification of sets of vertices using covering codes that uniquely identify single vertices we develop methods for constructing optimal topologies that yield identifying codes with a minimum number of codewords finally we describe an application of the theory developed in this paper to fault diagnosis of multiprocessor systems

sequences of optimal identifying codes locating faulty processors in a multiprocessor system gives the motivation for identifying codes denote by l the maximum number of simultaneously malfunctioning processors we show that if l spl ges 3 then the problem of finding the smallest cardinality of a 1 spl les l identifying code in a binary hypercube is equivalent to the problem of finding the smallest size of a 2l 1 fold 1 covering this observation yields infinite sequences of optimal identifying codes for every l l spl ges 3

sums of commutators in non commutative banach function spaces let m be a ii factor and denote by its normal faithful semi finite trace for any rearrangement invariant kothe function space x on 0 let x m be the associated non commutative banach function space this paper is concerned with ideals in m of the form ix m m x m that are contained in lp m for some p 0 it is proved that an element t in ix m is a finite sum of commutators of the form a b with a ix m and b m if and only if the function t 1t t t d t belongs to x where t is the brown spectral measure of t and t t t is the non increasing rearrangement of the function with respect to t this extends to general banach function spaces a result obtained by kalton for quasi banach ideals of compact operators and implies that the dixmier s trace of a quasi nilpotent element in l1 m is always zero

approximate equivalence for representations of c algebras and c dynamical systems abstract approximate equivalence unitary equivalence up to arbitrarily small compact perturbations is studied for representations of c algebras and covariant representations of c dynamical systems approximate equivalence for representations of c algebras is shown to be determined by a trace condition analogous to the trace condition for unitary equivalence of representations of finite groups for c dynamical systems with a compact abelian group acting approximate equivalence is shown to be determined by certain associated representations of the fixed point algebra of the action

connes s trace theorem for curved noncommutative tori application to scalar curvature in this paper we prove a version of connes s trace theorem for noncommutative tori of any dimension n 2 this allows us to recover and improve earlier versions of this result in dimensions n 2 and n 4 by fathizadeh and khalkhali we also recover connes s integration formula for flat noncommutative tori of mcdonald sukochev and zanin as a further application we prove a curved version of this integration formula in terms of the laplace beltrami operator defined by an arbitrary riemannian metric for the class of the so called self compatible riemannian metrics including the conformally flat metrics of connes and tretkoff this shows that connes s noncommutative integral allows us to recover the riemannian density this exhibits a neat link between this notion of noncommutative integral and noncommutative measure theory in the sense of operator algebras as an application of these results we set up a natural notion of scalar curvature for curved noncommutative tori

an analogue of the kato rosenblum theorem for commuting tuples of self adjoint operators suppose that a a 1 a n and are tuples of self adjoint operators on a hilbert space h such that and for all 1 j k n suppose that there are z 1 z n c r such that belongs to the trace class we prove that is unitarily equivalent to here and is the largest invariant subspace on which a can be simultaneously diagonalized modulo the trace class

commutator structure of operator ideals commutator structure of operator ideals ken dykema 1 tadeusz figiel gary weiss and mariusz wodzicki department of mathematics texas a m university college station tx 77843 3368 usa b instytut matematyczny polskiej akademii nauk 81 825 sopot poland department of mathematical sciences university of cincinnati cincinnati oh 45221 0025 usa department of mathematics university of california berkeley ca 94720 3840 usa

voiculescu theorem sobolev lemma and extensions of smooth algebras we present the analytic foundation of a unified b d f extension functor ext on the category of noncommutative smooth algebras for any frechet operator ideal k combining the techniques devised by arveson and voiculescu we generalize voiculescu s theorem to smooth algebras and frechet operator ideals a key notion involved is r smoothness which is verified for the algebras of smooth functions via a noncommutative sobolev lemma the groups ext are computed for many examples

singular integral operators and norm ideals satisfying a quantitative variant of kuroda s condition a norm ideal c is said to satisfy condition qk if there exist constants 0 t 1 and 0 b such that x k c bkt x c for every finite rank operator x and every k n where x k denotes the direct sum of k copies of x let be a regular borel measure whose support is contained in a unit cube q in rn and let kj be the singular integral operator on l2 rn with the kernel function xj yj x y 2 1 j n let qw w w be the usual dyadic decomposition of q i e qw w l is the dyadic partition of q by cubes of the size 2 l 2 l we show that if c satisfies qk and if w w2 w qw w w c where c is the dual of c 0 and w w w is any orthonormal set then k1 kn c this is a very general obstruction result for the problem of simultaneous diagonalization of commuting tuples of self adjoint operators modulo c

connes integration formula for the noncommutative plane our aim is to prove the integration formula on the noncommutative moyal plane in terms of singular traces a la connes

banach limits and traces on l1 abstract we introduce a new approach to traces on the principal ideal l 1 generated by any positive compact operator whose singular value sequence is the harmonic sequence distinct from the well known construction of j dixmier the new approach provides the explicit construction of every trace of every operator in l 1 in terms of translation invariant functionals applied to a sequence of restricted sums of eigenvalues the approach is based on a remarkable bijection between the set of all traces on l 1 and the set of all translation invariant functionals on l this bijection allows us to identify all known and commonly used subsets of traces dixmier traces connes dixmier traces etc in terms of invariance properties of linear functionals on l and definitively classify the measurability of operators in l 1 in terms of qualified convergence of sums of eigenvalues this classification has led us to a resolution of several open problems for the class l 1 from 7 as an application we extend connes classical trace theorem to positive normalised traces

comparison between algebraic and topological k theory of locally convex algebras abstract this paper is concerned with the algebraic k theory of locally convex c algebras stabilized by operator ideals and its comparison with topological k theory we show that if l is locally convex and j a frechet operator ideal then all the different variants of topological k theory agree on the completed projective tensor product l j and that the obstruction for the comparison map k l j k top l j to be an isomorphism is absolute algebraic cyclic homology we prove the existence of an exact sequence theorem 6 2 1 we show that cyclic homology vanishes in the case when j is the ideal of compact operators and l is a frechet algebra whose topology is generated by a countable family of sub multiplicative seminorms and admits an approximate right or left unit which is totally bounded with respect to that family theorem 8 3 3 this proves the generalized version of karoubi s conjecture due to mariusz wodzicki and announced in his paper m wodzicki algebraic k theory and functional analysis in first european congress of mathematics vol ii paris 1992 in progr math vol 120 birkhauser basel 1994 pp 485 496 we also consider stabilization with respect to a wider class of operator ideals called sub harmonic every frechet ideal is sub harmonic but not conversely for example the schatten ideal l p is sub harmonic for all p 0 but is frechet only if p 1 we prove a variant of the exact sequence above which essentially says that if a is a c algebra and j is sub harmonic then the obstruction for the periodicity of k a c j is again cyclic homology theorem 7 1 1 this generalizes to all algebras a result of wodzicki for h unital algebras announced in m wodzicki algebraic k theory and functional analysis in first european congress of mathematics vol ii paris 1992 in progr math vol 120 birkhauser basel 1994 pp 485 496 the main technical tools we use are the diffeotopy invariance theorem of cuntz and the second author which we generalize in theorem 6 1 6 and the excision theorem for infinitesimal k theory due to the first author

perturbation formulas for traces on normed ideals we prove perturbation results for traces on normed ideals in semifinite von neumann algebra factors this includes the case of dixmier traces in particular we establish existence of spectral shift measures with initial operators being dissipative or bounded and show that these measures can have singular components in the case of dixmier traces we also establish a linearization formula for a dixmier trace applied to perturbed operator functions a result that does not typically hold for normal traces

diagonalization and unitary equivalence modulo schatten p classes we give a necessary and sufficient condition for a commuting tuple a a1 an of self adjoint operators to be simultaneously diagonalizable modulo cp 1 p