integral mappings and the principle of local reflexivity for noncommutative l 1 spaces the operator space analogue of the strong form of the principle of local re exivity is shown to hold for any von neumann algebra predual and thus for any c algebraic dual this is in striking contrast to the situation for c algebras since for example k h does not have that property the proof uses the kaplansky density theorem together with a careful analysis of two notions of integrality for mappings of operator spaces

reflexive algebras with finite width lattices tensor products cohomology compact perturbations reflexive algebras play a central role in the study of general operator algebras for a reflexive algebra the associated invariant subspace lattice has structural importance analogous to that of the algebraic commutant in the study of algebras tomita s tensor product commutation theorem can be restated in the form alg l1 l2 alg l1 alg l2 where each li is a reflexive ortho lattice this same formula is proved for n fold tensor products in the setting when each li is a nest thus in particular a tensor product of nest algebras is again a reflexive algebra lance has shown that the hochschild cohomology of nest algebras vanishes modifications of his arguments show that cohomology vanishes for arbitrary csl algebras whose lattices are generated by finitely many independent nests this appears to be the strongest possible result in this direction the class of irreducible tridiagonal algebras with finite width commutative lattices is investigated and it is shown that these algebras have nontrivial first cohomology finally it is shown that if l is a finite width commutative subspace lattice and k is the set of compact operators then the quasitriangular algebra alg l k is closed in the norm topology this extends to arbitrary finite width csl algebras a result obtained for nest algebras by fall arveson and muhly

review of options for structural design sensitivity analysis part 1 linear systems the paper reviews options for structural design sensitivity analysis including global finite differences continuum derivatives discrete derivatives and computational or automated differentiation the objective is to put these different approaches to design sensitivity analysis in the context of accuracy and consistency computational cost and implementation options and effort linear static analysis and transient dynamic analysis are reviewed in a separate appendix special attention is paid to the semi analytical method a future paper will address design sensitivity analysis in nonlinear structural problems

a characterization of operator algebras abstract an operator algebra is a uniformly closed algebra of bounded operators on a hilbert space in this paper we give a characterization of unital operator algebras in terms of their matricial norm structure more precisely if a is an l matricially normed space and also an algebra with a completely contractive multiplication and an identity of norm 1 then there is a completely isometric isomorphism of a onto a unital operator algebra indeed the multiplication on a need not be assumed to be associative for this conclusion to follow examples are given to show that the condition on the identity is necessary it follows from the above that the quotient of an operator algebra by a closed two sided ideal with the natural matricial structure is again an operator algebra up to complete isometric isomorphism

factorization of completely bounded maps through reflexive operator spaces with applications to weak almost periodicity abstract let m be a hopf von neumann algebra so that m is a completely contractive banach algebra we investigate whether the product of two elements of m that are both weakly almost periodic functionals on m is again weakly almost periodic for that purpose we establish the following factorization result if m and n are injective von neumann algebras and if x y m n correspond to weakly compact operators from m to n factoring through reflexive operator spaces x and y respectively then the operator corresponding to xy factors through the haagerup tensor product x h y provided that x h y is reflexive as a consequence for instance for any hopf von neumann algebra m with m injective the product of a weakly almost periodic element of m with a completely almost periodic one is again weakly almost periodic

the slice map problem for weakly closed subspaces of von neumann algebras a a weakly closed subspace of b x is said to have propett s if for any a weakly closed subspace 5 of a von neumann algebra i x e 5 0 a r x for all rp e b 0 x l where r is the right slice map associated with t it is shown that semidiscrete von neumann algebras have property sa and various stability properties of the class of a weakly closed subspaces with property s0 are established it is also shown that if 111 g a is a w dynamical system such that k has property s0 and c is compact abelian then all of the spectral subspaces associated with a have property s0 some applications of these results to the study of tensor products of spectral subspaces and tensor products of reflexive algebras are given in particular it is shown that if l is a commutative subspace lattice with totally atomic core and l is an arbitrary subspace lattice then alg i 0 e2 algc1 0 algl 2 introduction slice maps introduced by tomiyama have proved to be a powerful tool in studying tensor products of c algebras and von neumann algebras see e g 23 24 26 281 in this paper we use slice maps to study tensor products of a weakly closed subspaces of von neumann algebras particularly tensor products of spectral subspaces and tensor products of reflexive algebras if t and 6 are von neumann algebras then for each qp in x the predual of x there is a unique a weakly continuous linear map r from 9dz 0 9 to 6 such that r w a x b a q b a e 91r b e dl l called the right slice map associated with p similarly for each 4 e 9l there is a left slice map li from 9dth0 6 to 9dt if 5 c 9th and y c are a weakly closed subspaces and 5 8 5 denotes the a weak closure of the algebraic tensor product of 5 and c it is clear that if x e 0 0 then r x c 9 for all p e 9 x if x e 5 0 r x efor all qg e 5 received by the editors february 19 1982 and in revised form july 20 1982 1980 mathematics subject classification primary 46l10 46l55 46m05 47d25

operator space tensor products and inductive limits abstract we investigate whether the tensor product of operator spaces which includes the operator space projective haagerup and schur tensor products and the tensor product of operator systems commute with inductive limits in the sense that if x n n is an inductive system of operator spaces or operator systems with an inductive limit x and if y is any operator space or operator system then whether x n y n id becomes an inductive system and if so whether the inductive limit of this system is same as x y where denotes the tensor product of operator spaces or operator systems we also discuss about the bidual of such an inductive limit and obtain embeddings lim x n y lim x n y under certain restrictions

modules over operator algebras and the maximal c dilation abstract we continue our study of the general theory of possibly nonselfadjoint algebras of operators on a hilbert space and modules over such algebras developing a little more technology to connect nonselfadjoint operator algebra with the c algebraic framework more particularly we make use of the universal or maximal c algebra generated by an operator algebra and c dilations this technology is quite general however it was developed to solve some problems arising in the theory of morita equivalence of operator algebras and as a result most of the applications given here and in a companion paper are to that subject other applications given here are to extension problems for module maps and characterizations of c algebras

almost completely isometric embeddings between preduals of von neumann algebras abstract we will prove that if the predual of an injective von neumann algebra is embedded in the predual of another von neumann algebra almost completely isometrically then it is complemented almost completely contractively this result is the operator space analogue of dor s theorem

vector valued hausdorff young inequality on compact groups the main purpose of this paper is to study the validity of the hausdorff young inequality for vector valued functions defined on a non commutative compact group as we explain in the introduction the natural context for this research is that of operator spaces this leads us to formulate a whole new theory of fourier type and cotype for the category of operator spaces the present paper is the first step in this program where the basic theory is presented the main examples are analyzed and some important questions are posed

approximation properties for group algebras and group von neumann algebras let g be a locally compact group let c g resp vn g be the c algebra resp the von neumann algebra associated with the left regular representation i of g let a g be the fourier algebra of g and let moa g be the set of completely bounded multipliers of a g with the completely bounded norm moa g is a dual space and we say that g has the approximation property ap if there is a net ua of functions in a g with compact support such that ua a 1 in the associated weak topology in particular g has the ap if g is weakly amenable a g has an approximate identity that is bounded in the completely bounded norm for a discrete group f we show that f has the ap x c f has the slice map property for subspaces of any c algebra x vn jt has the slice map property for a weakly closed subspaces of any von neumann algebra property se the semidirect product of weakly amenable groups need not be weakly amenable we show that the larger class of groups with the ap is stable with respect to semidirect products and more generally this class is stable with respect to group extensions we also obtain some results concerning crossed products for example we show that the crossed product m a g of a von neumann algebra m with property s by a group g with the ap also has property s

a note on polylogarithms on curves and abelian schemes in this note we study the polylogarithm extension on curves and abelian schemes in the etale realization the main result shows that the polylog on the jacobian of a curve is given as the cup product of the polylog on the curve with the fundamental class of the curve

henrici s transformation and its application to the computation of derivatives of eigensystems in this paper we examine the application of henrici s transformation to a sequence of vectors generated by a simultaneous iteration method for computing the partial derivatives of eigenvalues and eigenvectors of parameter dependent matrices numerical results support our theoretical analysis and indicate that henrici s method compares favorably with other vector sequence transformation methods

exactness of locally compact groups we give some new characterizations of exactness for locally compact second countable groups in particular we prove that a locally compact group is exact if and only if it admits a topologically amenable action on a compact hausdorff space this answers an open question by anantharaman delaroche

lovasz theta type norms and operator systems abstract to each graph on n vertices there is an associated subspace of the n n matrices called the operator system of the graph we prove that two graphs are isomorphic if and only if their corresponding operator systems are unitally completely order isomorphic this means that the study of graphs is equivalent to the study of these special operator systems up to the natural notion of isomorphism in their category we define new graph theory parameters via this identification certain quotient norms that arise from studying the operator system of a graph give rise to a new family of parameters of a graph we then show basic properties about these parameters and write down explicitly how to compute them via a semidefinite program and discuss their similarities to the lovasz theta function finally we explore a particular parameter in this family and establish a sandwich theorem that holds for some graphs

the hodge realization of the polylogarithm on the product of multiplicative groups the purpose of this article is to describe explicitly the polylogarithm class in absolute hodge cohomology of a product of multiplicative groups in terms of the bloch wigner ramakrishnan polylogarithm functions we will use the logarithmic dolbeault complex defined by burgos to calculate the corresponding absolute hodge cohomology groups

mode tracking issues in structural optimization within the context of optimization of the structural dynamics properties of finite element models methodology is developed for the tracking of eigenpairs through changes in the structural eigenvalue problem the goal is to eliminate difficulties caused by mode switching i e frequency crossing out of several candidate methods two methods for mode tracking are successful the first method the higher order eigenpair perturbation algorithm is based on a perturbation expansion of the eigenproblem it iteratively computes changes in the eigenpairs due to parameter perturbations with the important feature of maintaining the correspondence between the baseline and perturbed eigenpairs the second method is a cross orthogonality check method which uses mass orthogonality to reestablish correspondence after a standard reanalysis modified eigenpair extraction routines lanczos subspace iteration inverse power were unsuccessful in tracking modes applications of mode tracking technology that are presented are frequency constrained optimization and optimization with mode shape constraints each application procedure is outlined and examples are given recommendations are made based on method efficiency and robustness in the example problems

the tensor product problem for reflexive algebras it was observed by gilfeather hopenwasser and larson in 1 that tomita s commutation formula for tensor products of von neumann algebras can be rewritten in a way that makes sense for tensor products of arbitrary reflexive algebras the tensor product problem for reflexive algebras is to decide for which pairs of reflexive algebras this tensor product formula is valid recall that a subalgebra jtf of the algebra b 3p of all bounded operators on a hubert space is said to be a von neumann algebra if it is closed in the weak operator topology contains the identity operator i and is self adjoint i e a t implies a e j the commutant j of jt is the set of all operators b e b such that ba ab for all a e jf the commutant of a von neumann algebra is again a von neumann algebra moreover it follows from von neumann s double commutant theorem that a self adjoint subalgebra jf of b j f is a von neumann algebra if and only if jf jf let jf c b jr and jv c b x be von neumann algebras and let 3t denote the hilbert space tensor product of f and 3 if a e jf and b jv there is a unique operator a b in bffi 3t such that a b x y ax by for all x e and j g j the von neumann algebra generated by a b a e j and b e j is denoted by j j tomita s commutation theorem asserts that for any pair of von neumann algebras j and jf the following commutation formula is valid

equivalence of normal states on von neumann algebras and the flow of weights abstract let m be a von neumann algebra two positive normal functionals on m are called equivalent if is in the norm closure of the orbit of under the action of inner automorphisms our main result is an isometric characterization of the quotient space m we construct a natural isometry a g4 of m into the set of positive normal functionals on the smooth flow of weights of m where the smooth flow of weights is realized as the center z n of the crossed product n m r for some faithful normal semifinite weight on m as an application we obtain that an automorphism on a factor m with separable predual acts trivially on m if and only if acts trivially on the smooth flow of weights i e the connes takesaki modulus mod of vanishes we also obtain a new proof of the diameter formula diam s n m 2 1 1 for the quotient of the state space of a factor of type iii 0 1

an operator space approach to condition c abstract we show that there exists a natural embedding from the tensor product v w of the biduals of operator spaces v and w into the bidual v w of the injective tensor product of v and w which is separately weak continuous from this we define condition c for operator spaces

techniques for generating analytic covariance expressions for eigenvalues and eigenvectors one of the key problems in data fusion is the estimation of a parameter vector from a set of noisy measurements in many cases the optimal estimate of such a parameter vector can be solved through the least squares problem there are however a number of important problems whose solution instead takes the form of an eigenvalue eigenvector problem furthermore knowledge of the uncertainty of the optimal estimate is as important as the estimate itself for many practical applications and this uncertainty is typically captured in the form of a covariance matrix while the covariance matrix for a least squares estimate has been well studied there has been substantially less research on the covariance of an optimal estimate originating from an eigenvalue eigenvector problem in this paper we develop general expressions that determine the uncertainty in a vector estimate obtained from an eigenvalue eigenvector problem given the uncertainty of the matrix this includes developing expressions for the analytic derivatives of the eigenvalues and eigenvectors with respect to the matrix from which they come finally the techniques developed are numerically validated with forward finite differencing and a monte carlo analysis and then used to determine covariance expressions for an ellipse fitting technique and the estimation of attitude quaternions

completely bounded module maps and the haagerup tensor product abstract we obtain a representation theorem for module maps defined on the algebra k h of compact operators this is used to show that the haagerup tensor product of two operator algebras enjoys strong versions of tomita s commutant theorem and the slice map property we also give a general theorem concerning the automatic complete boundedness of module maps

self duality for the haagerup tensor product and hilbert space factorizations d blecher and v paulsen showed that the haagerup tensor product v h w for operator spaces v and w preserves inclusions it is proved to also preserve complete quotient maps and to be self dual in the sense that it induces the haagerup norm on the algebraic tensor product v w the full operator dual space v h w is computed it coincides with the natural operator space gg2 v w of maps v w which have completely bounded factorizations through hilbert spaces with vectors identified with row matrices more generally one has the natural complete isometry gg2 v h w x gg2 v gg2 w x given hilbert spaces h and k with vectors regarded as column matrices it is shown that one may identify the operator spaces b h k and cb h k

bilinear ideals in operator spaces abstract we introduce a concept of bilinear ideal of jointly completely bounded mappings between operator spaces in particular we study the bilinear ideals n of completely nuclear i of completely integral and e of completely extendible bilinear mappings we also consider the multiplicatively bounded bilinear mappings mb and its symmetrization smb we prove some basic properties of them one of which is the fact that i is naturally identified with the ideal of linear completely integral mappings on the injective operator space tensor product

amplification of completely bounded operators and tomiyama s slice maps abstract let m n be a pair of von neumann algebras or of dual operator spaces with at least one of them having property s and let be an arbitrary completely bounded mapping on m we present an explicit construction of an amplification of to a completely bounded mapping on m n our approach is based on the concept of slice maps as introduced by tomiyama and makes use of the description of the predual of m n given by effros and ruan in terms of the operator space projective tensor product cf effros and ruan internat j math 1 2 1990 163 j operator theory 27 1992 179 we further discuss several properties of an amplification in connection with the investigations made in may et al arch math basel 53 3 1989 283 where the special case m b h and n b k has been considered for hilbert spaces h and k we will then mainly focus on various applications such as a remarkable purely algebraic characterization of w continuity using amplifications as well as a generalization of the so called ge kadison lemma in connection with the uniqueness problem of amplifications finally our study will enable us to show that the essential assertion of the main result in may et al 1989 concerning completely bounded bimodule homomorphisms actually relies on a basic property of tomiyama s slice maps

tensor products of operator spaces abstract in this paper we lay the foundations for a systematic study of tensor products of subspaces of c algebras to accomplish this various notions of duality are introduced and employed elementary proofs of the complete injectivity of the haagerup norm and of the extension theorem for completely bounded maps are given pisier s gamma norms are examined and found to be special cases of the haagerup norm we identify the greatest operator space cross norm and show that the spatial tensor norm is the least operator space cross norm in an appropriate sense indeed most of the elementary theory of banach space tensor norms generalizes to the category of operator spaces

on multiple eigenvalues of matrices depending on several parameters the eigenvalues and eigenvectors as well as their derivatives of matrices depending on one or several parameters have been studied by sun j comput math 3 1985 pp 351 364 using the implicit function theorems and others but not for the more general multiple eigenvalues in this paper the mean of the multiple eigenvalues in terms of the trace operator tr the corresponding invariant subspaces and their derivatives are studied using a generalization of sun s approach the numerical aspects concerning the computation of such derivatives by direct and iterative methods e g simultaneous and inverse simultaneous iterations will be discussed briefly the main results in this paper apply to clusters of nonmultiple eigenvalues as well the implications e g on simultaneous iteration will be explored

dilation theory and systems of simultaneous equations in the predual of an operator algebra ii 1 this note is a continuation of our earlier paper 3 in which we developed a dilation theory for a certain class of contraction operators acting on a separable infinite dimensional complex hilbert space the notation and terminology in what follows is taken from 3 for the convenience of the reader we recall a few pertinent definitions the algebra of bounded linear operators on is denoted by y if t se 2c the ultraweakly closed algebra generated by t and l e is denoted by dr we recall that d r can be identified with the dual space of the quotient space q r z c where zc denotes the ideal of trace class operators in 5 24 and is the preannihilator of d r in z c under the pairing

tensor products of operator systems abstract the purpose of the present paper is to lay the foundations for a systematic study of tensor products of operator systems after giving an axiomatic definition of tensor products in this category we examine in detail several particular examples of tensor products including a minimal maximal maximal commuting maximal injective and some asymmetric tensor products we characterize these tensor products in terms of their universal properties and give descriptions of their positive cones we also characterize the corresponding tensor products of operator spaces induced by a certain canonical inclusion of an operator space into an operator system we examine notions of nuclearity for our tensor products which on the category of c algebras reduce to the classical notion we exhibit an operator system s which is not completely order isomorphic to a c algebra yet has the property that for every c algebra a the minimal and maximal tensor product of s and a are equal

representations of completely bounded multilinear operators a deli ion of a completely bounded multilinear operator from one c algebra into another is introduced each completely bounded multilinear operator from a algebra into the algebra of bounded linear operators on a hilbert space is shown to be representable in terms of representations of the c algebra and interlacing operators this result extends wittstock s theorem that decomposes a completely bounded linear operator from a c algebra into an injective c algebra into completely positive linear operators 0 1987 academic press inc stinespring s theorem gives a useful representation for a completely positive linear operator from a c algebra into the algebra bl h for continuous linear operators on a hilbert space h 12 11 using this representation with wittstock s theorem that decomposes a completely bounded linear operator as a finite linear combination of completely positive linear operators 14 lo one obtains a representation of a completely bounded linear operator from a c algebra into bl h our main result is a representation theorem for completely bounded multilinear operators from a c algebra into bl h which generalizes this representation of completely bounded linear operators corollaries give multilinear generalizations of several results known for completely bounded linear operators we shall briefly describe the type of representations to be 151

multipliers of the fourier algebras of some simple lie groups and their discrete subgroups for any amenable locally compact group g the space of multipliers ma g of the fourier algebra a g coincides with the space b g of functions on g that are linear combinations of continuous positive definite functions we prove that ma g b g 0 for many non amenable connected groups more specifically we prove that moa g b g 0 for the classical complex lie groups and the general lorentz groups soo n 1 n 2 moa g is a certain subspace of ma g which we call the space of completely bounded multipliers of a g unlike ma g the space moa g has nice stability properties with respect to direct products of groups it is known that the fourier algebra of the free group on n generators n 2 2 admits an unbounded approximate unit pn which is bounded in the multiplier norm we extend this result to any closed subgroup of the general lorentz group soo n 1 moreover we show that for these groups pn can be chosen to be bounded with respect to the moa g norm by a duality argument we obtain that the reduced c algebra of every discrete subgroup of soo n 1 has the completely bounded approximation property in particular this property holds for c f2 the reduced c algebra of the free group on two generators we also prove

calculation of eigenvector derivatives for structures with repeated eigenvalues in structural optimization and system identification eigenvector derivatives provide important information for updating design model parameters when the current parameter values yield repeated eigenvalues it has not been possible previously to calculate unique eigenvector derivatives recent work has provided a method for determining unique eigenvalue derivatives for this case but methods for calculating the eigenvector sensitivities have been incomplete in this work a complete method for calculation of repeated root eigenvector derivatives is shown for the real symmetric structural eigenproblem the derivation is completed by using information from the second derivative of the eigen problem and is limited to the case of distinct eigenvalue sensitivities as an example the repeated root eigenvector sensitivities are calculated for a simple three degree of freedom beam grillage comparisons of linear approximations using these derivatives to the calculated eigenvectors support the accuracy of the formulation

representations of function algebras abstract operator spaces and banach space geometry let g be the closed unit ball of some norm on cn and let a g be the closure of the polynomials in the sup norm we prove that if n 5 then there is a contractive representation of a g as operators on a hilbert space which is not completely contractive our technique involves introducing a numerical invariant x for a normed space x which measures the difference between the minimal operator space structure which can be assigned to x min x and the maximal structure max x we estimate x using banach space techniques we also prove that if x is any infinite dimensional subspace of the space of continuous functions on a compact hausdorff space then there exists a bounded linear map on x which is not completely bounded

the slice map problem and approximation properties we show that a weakly closed subspace j of the bounded operators bh on an infinite dimensional hilbert space h has property s the fubini product lt l for all weakly closed subspaces t b h if and only if j satisfies a certain approximation property which we call the weak approximation property the weak approximation property is implied by but does not imply the weak completely bounded approximation property moreover if j has the weak approximation property then the predual j has the approximation property for banach spaces we also prove analagous results for property s and variations of property s for c algebras as an application of our characterization of subspaces with property s we show that the reflexive algebra tensor product formula alg l1 alg l2 alg l1 l2 is not always valid in fact we show that for each of the types ii1 ii and iii 0 1 there is a separably acting factor m alg l1 of that type and a reflexive algebra a alg l2 such that alg l1 alg l2 is strictly contained in alg l1 l2

extensions of locally compact quantum groups and the bicrossed product construction abstract in the framework of locally compact quantum groups we study cocycle actions we develop the cocycle bicrossed product construction starting from a matched pair of locally compact quantum groups we define exact sequences and establish a one to one correspondence between cocycle bicrossed products and cleft extensions in this way we obtain new examples of locally compact quantum groups

on the morita equivalence of tensor algebras our objective is two fold first we want to develop a notion of morita equivalence for c correspondences that guarantees that if two c correspondences e and f are morita equivalent then the tensor algebras of e and f taoeu and taofu are strongly morita equivalent in the sense of 8 the toeplitz algebras toeu and tofu are strongly morita equivalent in the sense of rieffel 32 see 33 also and the cuntz pimsner algebras 28 ooeu and oofu are strongly morita equivalent in the same sense we were inspired by earlier work of curto williams and the first author in 15 and combes 14 these papers investigate conditions implying that the crossed product of two c dynamical systems are strongly morita equivalent given that the coefficient algebras are strongly morita equivalent abadie eilers and exel 1 were similarly inspired and developed a theory of morita equivalence for special c correspondences our analysis extends theirs but our arguments are different see example 2 5 and remarks 3 3 and 3 6 for a comparison of their results and ours second we want to investigate the converse implication that is we study the following question if taoeu and taofu are strongly morita equivalent in the sense of 8 when are e and f morita equivalent in the sense we define for this converse direction we focus on the tensor algebras rather than the toeplitz and cuntz pimsner algebras because very little can be said in the self adjoint setting here we were inspired by arveson s paper 2 in which it is proved that two ergodic measure preserving transformations are conjugate if and only if certain non self adjoint crossed products associated with the transformations are algebraically isomorphic see 3 also his analysis was further extended by k saito and the first author to cover non self adjoint crossed products built from automorphisms of general von neumann algebras they showed that non self adjoint crossed products built from properly outer automorphisms of von neumann algebras are isomorphic if and only if the automorphisms are conjugate see 22 and 23 our principal result in the converse direction theorem 7 2 asserts that if e and f are two aperiodic correspondences and if taoeu is strongly morita equivalent to taofu in the sense of 8 then e and f are morita equivalent as we shall see in 5 the notion of aperiodicity is an exact analogue for correspondences of the concept of free action in ergodic theory free action was a central hypothesis in arveson s

some counterexamples in nonselfadjoint algebras in this note a construction is given of a special operator t on hilbert space a free variable in this construction is a weakly closed subspace ty of operators by appropriate choice of j we give counterexamples to several well known

interpolation of operator spaces abstract we develop the real interpolation theory for operator spaces we show that the main theorems in the classical real interpolation theory for banach spaces hold in our operator space setting these include the equivalence duality and reiteration theorems as an application of the duality theorem we prove that the real interpolation operator space of parameters 1 2 2 between an operator space and its antidual is completely isomorphic to an operator hilbert space oh i discovered recently by g pisier we also present an outline of a general interpolation theory in the category of operator spaces in particular we construct the operator space version of the orbit and coorbit functors and extend to operator spaces the classical aronzsajn gagliardo theorem our development complements some recent works of pisier

amenability of hopf von neumann algebras and kac algebras abstract let m be a hopf von neumann algebra the operator predualm ofmis a completely contractive banach algebra with multiplicationm m m m we call m operator amenableif the completely contractive banach algebram isoperator amenable i e for every operatorm bimodulev every completely bounded derivation fromm into the dualm bimodulev is inner there is a weaker notion of amenability introduced by d voiculescu we say that a hopf von neumann algebra m isvoiculescu amenableif there exists a left invariant mean onm we show that if a hopf von neumann algebra m is operator amenable then it is voiculescu amenable for kac algebras there is astrong voiculescu amenability we show that for discrete kac algebras these amenabilities are all equivalent in fact if we letk m be a discrete kac algebra and letk m be its compact dual kac algebra then the following are equivalent 1 kis operator amenable 2 kis voiculescu amenable 3 the von neumann algebramis hyperfinite 4 kis strong voiculescu amenable 5 kis operator amenable 6 m has a bounded approximate identity

a polynomially bounded operator on hilbert space which is not similar to a contraction let e 0 we prove that there exists an operator te e2 2 such that for any polynomial p we have iip te ii not similar to a contraction i e there does not exist an invertible operator s f2 e f2 such that jis 1tesii tributed to halmos after his well known 1970 paper ten problems in hilbert space we also give some related finite dimensional estimates department of mathematics texas a m university college station texas 77843 universite paris vi equipe d7analyse case 186 75252 paris cedex 05 france e mail address gipqccr jussieu fr this content downloaded from 157 55 39 104 on sun 19 jun 2016 06 52 47 utc all use subject to http about jstor org terms

completely bounded multipliers of the fourier algebra of a simple lie group of real rank one the fourier algebra a g of a locally compact group g is the space of matrix coefficients of the regular representation and is the predual of the yon neumann algebra vn g generated by the regular representation of g on l 2 g a multiplier m of a g is a bounded operator on a g given by pointwise multiplication by a function on g also denoted m we say m is a completely bounded multiplier ofa g if the transposed operator on vn g is completely bounded definition below it may be possible to find a net ofa g functions m i ie i say such that mi tends to

operator synthesis and tensor products we show that kraus property s is preserved under taking weak closed sums with masa bimodules of finite width and establish an intersection formula for weak closed spans of tensor products one of whose terms is a masabimodule of finite width we initiate the study of the question of when operator synthesis is preserved under the formation of products and prove that the union of finitely many sets of the form where is a set of finite width while is operator synthetic is under a necessary restriction on the sets again operator synthetic we show that property s is preserved under spatial morita subordinance

multilinear maps and tensor norms on operator systems abstract we extend work of christensen and sinclair on completely bounded multilinear forms to the case of subspaces of c algebras and obtain a representation theorem and a hahn banach extension theorem for such maps in the second part of the paper the haagerup norms on tensor products are investigated and we obtain new characterizations of these quantities

ein operatorwertiger hahn banach satz abstract we generalize arveson s extension theorem for completely positive mappings 1 to a hahn banach principle for matricial sublinear functionals with values in an injective c algebra or an ideal in b h we characterize injective w algebras by a matricial order condition we illustrate the matricial hahn banach principle by three applications 1 let a b b be unital c algebras b a subalgebra of a and b b injective if a b is a completely bounded self adjoint b bihomomorphism then it can be expressed as the difference of two completely positive b bihomomorphism 2 let m be a w algebra containing 1 h on a hilbert space h if m is finite and hyperfinite there exists an invariant expectation mapping p of b h onto m p is an extension of the center trace 3 combes 7 proved that a lower semicontinuous scalar weight on a c algebra is the upper envelope of bounded positive functionals we generalize this result to unbounded completely positive mappings with values in an injective w algebra

computation of derivatives of repeated eigenvalues and corresponding eigenvectors by simultaneous iteration an earlier simultaneous iteration method for computing derivatives of eigenvalues and the corresponding eigenvectors of nonsymmetric matrices depending smoothly on some real parameters is extended to the case of repeated eigenvalues

subspaces of c algebras abstract basic properties of matricially normed spaces are considered and a simple matrix norm characterization of the subspaces of c algebras is given the latter result is used to study the haagerup tensor products and quotients of such subspaces