a continuum model accounting for defect and mass densities in solids with inelastic material behaviour in this paper the analysis of structures with inelastic material behaviour is considered taking into account the evolution of defects and changes in mass density the underlying kinematical concept of an oriented continuum is general enough to describe the micro and macrobehaviour of material bodies appropriately based on the logical and consistent variational arguments for a lagrangian functional the dynamic balance laws boundary and transversality conditions all related to the evolution of defect density and mass changes are derived for macro and microstresses of deformational as well as of configurational type the adopted procedure which formally leaves the balance laws unaltered leads to the additional balance law for changes in defect density and additional boundary conditions for the changes in mass and defect densities driving forces or affinities associated with the evolution of defect and mass densities and a generalization of the j integral representing the thermodynamic forces on defects are obtained a nonlocal constitutive model accounting for changes in the defect density is presented

on the continuity of the map ϑ ϑ from the predual of a w algebra abstract let be elements in the predual of a w algebra for their absolute value parts the estimate 2 1 2 is obtained

a constitutive frame of elastoplasticity at large strains based on the notion of a plastic metric abstract the article presents a constitutive framework of large strain elastoplasticity in both the lagrangian and the eulerian geometric setting which takes into account anisotropic material response in summary the key ingredients of this framework are i the introduction of a plastic metric which is assumed to describe locally the history dependent inelastic material response in the sense of an internal variable formulation ii the definition of a convex elastic domain in the space of the local stress like variable conjugate to the plastic metric denoted as the plastic force iii an equivalent lagrangian and eulerian representation of all constitutive functions as isotropic tensor functions in terms of an extended set of arguments denoted as anisotropy variables iv the set up of normality rules for the evolution of the plastic metric and the anisotropy variables yielding a canonical symmetric form of the elastoplastic tangent moduli v a geometrically exact decomposition of the set of constitutive equations into possibly decoupled volumetric and isochoric contributions applications of the constitutive framework are demonstrated by means of several conceptual model problems which cover isotropic initial anisotropic and induced anisotropic elastoplastic response

inequality between powers of positive semidefinite matrices abstract for p 1 we present reasonable nonnegative functions f t on 0 such that in the space of matrices 0 a b and b f a imply b p a p

on the extension of linear contractions some results of the hahn banach type resume let be a norm on rn and s a compact convex semigroup of linear contractions given two k tuples of n vectors x 1 x k and y 1 y k we seek conditions for the existence of a contraction s s that simultaneously takes x i to y i that is sx i y i for all i 1 k straightforward application of the separation theorem for convex sets provides a general but abstract result in the form of a system of inequalities specializing to the 1 norm and the norm respectively and s to comprise either all contractions or those contractions that preserve a particular linear form it is possible to evaluate the characteristic functionals arising from the separation theoem therby the abstract results can be rduced to a tractable form which turns out to be of the hahn banach type

the cone of lower semicontinuous traces on a c algebra the cone of lower semicontinuous traces is studied with a view to its use as an invariant its properties include compactness hausdorffness and continuity with respect to inductive limits a suitable notion of dual cone is given the cone of lower semicontinuous 2 quasitraces on a non exact c algebra is considered as well these results are applied to the study of the cuntz semigroup it is shown that if a c algebra absorbs the jiang su algebra then the subsemigroup of its cuntz semigroup consisting of the purely non compact elements is isomorphic to the dual cone of the cone of lower semicontinuous 2 quasitraces this yields a computation of the cuntz semigroup for the following two classes of c algebras c algebras that absorb the jiang su algebra and have no non zero simple subquotients and simple c algebras that absorb the jiang su algebra 1 introduction the most standard invariants in the classification of nu clear c algebras are their k groups and their traces the traces at least for simple c algebras are assumed to be bounded in the unital case and lower semicontinuous and densely finite in the non unital case if one has in mind the classification of non simple c algebras it is clear that these two kinds of traces will not suffice and a broader class should be considered in this paper we study the properties of the cone of all lower semicontinuous traces on a c algebra with the purpose of applying our results to questions in the classification of non simple c algebras one sign that this is natural is that this cone in particular determines the lattice of closed two sided ideals an important invariant in its own right see 3 4 we shall also consider lower semicontinuous 2 quasitraces since these appear naturally as functionals on the cuntz semigroup of the algebra if the

spectral inequalities for matrix exponentials abstract this note generalizes an inequality of bernstein as follows if c is an n n complex matrix and c k is the k th compound of c 1 k n n n k and if the eigenvalues of c k are labeled in order of decreasing magnitude 1 c k 2 c k n c k define the partial trace tr k i c by tr k i c h 1 i h c k i 1 n then for any complex n n matrix a tr k i e a e a tr k i e a a i 1 n with equality if a is normal or k n a spectral inequality of k fan is also generalized through the use of compound matrices

triangular truncation and finding the norm of a hadamard multiplier for b a fixed matrix we study the problem of using a criterion of haagerup to find the norm of the map a a b where is the hadamard or entrywise product of matrices the techniques developed are applied to triangular truncation and it is proved that if kn is the norm of triangular truncation of n n matrices then knlogn 1

an extremal problem in fourier analysis with applications to operator theory a certain minimal extrapolation problem for fourier transforms is known to have consequences for the determination of best possible bounds in some problems in linear operator equations and in perturbation of operators in this paper we estimate the value of the constant in the fourier transform problem by an analytic reformulation

when is the clifford algebra of a binary cubic form split let u v be a nondegenerate binary form over a field f of characteristic not two or three we prove that the clifford algebra of u v over f is split if and only if the ternary form w3 u v has a nontrivial f rational point

a generalization of a a 1 i abstract a matrix inequality is obtained in an elementary way for the schur product of two positive definite matrices the inequality generalizes a well known result due to fiedler which asserts that if a is a positive definite matrix then a a 1 i is a positive semidefinite matrix where denotes the schur multiplication

holder type norm inequalities for schur products of matrices abstract for a unitarily invariant norm on m n and p 1 we define a p by a p 1 p then p is again a unitarily invariant norm we give holder type inequalities for schur products of the form a b 0 p0 a 1 p1 b 2 p2 as a corollary we settle in a stronger form a conjecture of marcus et al on submultiplicativity of a unitarily invariant norm with respect to schur multiplication we prove also holder type inequalities for operator radii w of the form w a b w a w b

some majorization inequalities induced by schur products in euclidean jordan algebras abstract in a euclidean jordan algebra v of rank n an element x is said to be majorized by an element y symbolically x y if the corresponding eigenvalue vector x is majorized by y in r n in this article we describe pointwise majorization inequalities of the form t x s x where t and s are linear transformations induced by schur products specializing we recover analogs of majorization inequalities of schur hadamard and oppenheimer stated in the setting of euclidean jordan algebras as well as majorization inequalities connecting quadratic and lyapunov transformations on v we also show how schur products induced by certain scalar means such as arithmetic geometric harmonic and logarithmic means naturally lead to majorization inequalities

on the norm of a schur product abstract if a x is the schur product of n n matrices a and x then we study estimates on the norm of the map x a x where x has the norm it acquires as a linear operator on a complex n dimensional hilbert space

a shell finite element for large strain elastoplasticity with anisotropies part ii constitutive equations and numerical applications abstract an eight node c 0 shell element for finite elastic plastic deformations with anisotropies is developed it combines the advantages of an isoparametric description of geometry and deformation the application of tensors in cartesian components and a real and effective plane stress description with three displacement and three director degrees of freedom at each node in part i of the paper the shell theory including the kinematics the variational principle the application of lagrange multipliers with their condensation on the element level and a comparative study of various assumed strain techniques were presented and the results of convergence tests given in this paper we consider the constitutive equations for large elastic and large plastic strains accounting for initial and induced anisotropies and the corresponding thermodynamics then we investigate the return algorithm for finite strains and the implementation of the element procedure including stiffness matrix and residual force vector finally we present the results of extended numerical applications and a comparison with fe solutions published in the literature as far as such are available

the dixmier property and tracial states for c algebras a t was partially supported by an nserc postdoctoral fellowship and through the epsrc grant ep n00874x 1 acknowledgements we are grateful to luis santiago for helpful discussions at an early stage of this investigation we would also like to thank the referee for providing helpful comments which have led to a number of improvements

convex hulls of unitary orbits of normal elements in c algebras with tracial rank zero abstract let a be a unital separable simple c algebra with tracial rank zero and let x y a be two normal elements we show that x is in the closure of the convex hull of the unitary orbit of y if and only if there exists a sequence of unital completely positive linear maps n from a to a such that the sequence n y converges to x in norm and also approximately preserves the trace values a purely measure theoretical description for normal elements in the closure of the convex hull of unitary orbit of y is also given in the case that a has a unique tracial state some classical results about the closure of the convex hull of the unitary orbits in von neumann algebras are proved to hold in the c algebraic setting

infinite non simple c algebras absorbing the cuntz algebra o abstract the first named author has given a classification of all separable nuclear c algebras a that absorb the cuntz algebra o we say that a absorbs o if a is isomorphic to a o motivated by this classification we investigate here if one can give an intrinsic characterization of c algebras that absorb o this investigation leads us to three different notions of pure infiniteness of a c algebra all given in terms of local algebraic conditions on the c algebra the strongest of the three properties strongly purely infinite is shown to be equivalent to absorbing o for separable nuclear c algebras that either are stable or have an approximate unit consisting of projections in a previous paper 2000 amer j math 122 637 666 we studied an intermediate and perhaps more natural condition purely infinite that extends a well known property for simple c algebras the weakest condition of the three weakly purely infinite is shown to be equivalent to the absence of quasitraces in an ultrapower of the c algebra the three conditions may be equivalent for all c algebras and we prove this to be the case for c algebras that are either simple of real rank zero or approximately divisible

clifford algebras of binary homogeneous forms abstract we study the generalized clifford algebras associated to homogeneous binary forms of prime degree p focusing on exponentiation forms of p central spaces in division algebra for a two dimensional p central space we make the simplifying assumption that one basis element is a sum of two eigenvectors with respect to conjugation by the other if the product of the eigenvalues is 1 then the clifford algebra is a symbol azumaya algebra of degree p generalizing the theory developed for p 3 furthermore when p 5 and the product is not 1 we show that any quotient division algebra of the clifford algebra is a cyclic algebra or a tensor product of two cyclic algebras and every product of two cyclic algebras can be obtained as a quotient explicit presentation is given to the clifford algebra when the form is diagonal

furuta s inequality and its application to ando s theorem abstract as a continuation of preceding notes we discuss furuta s inequality under the chaotic order defined by log a log b for positive invertible operators a and b which is applied to a generalization of ando s theorem consequently we obtain furuta s inequality under the chaotic order

majorization between the diagonal elements and the eigenvalues of an oscillating matrix abstract in this note we give an answer to an open question posed by marshall and olkin on the majorization between the diagonal elements and the eigenvalues of an oscillating matrix

an operator inequality abstract for hilbert space operators with s invertible hermitian it is proved that sts 1 s 1 ts 2 t

induced norms of the schur multiplier operator abstract fix an n by n complex matrix a and consider the operator x sa x a x on n by n complex matrices x where a x denotes the schur product of a and x we show that the induced norm of sa with respect to the numerical radius norm is at most one if and only if the matrix a admits a factorization a b wb where w is a contractive matrix and the euclidean norms of the columns of b are at most one we give other equivalent characterizations and derive as a consequence a formally similar result about the induced norm of sa with respect to the spectral norm

the geometry of ulrich bundles on del pezzo surfaces abstract given a smooth del pezzo surface x d p d of degree d we isolate the essential geometric obstruction to a vector bundle on x d being an ulrich bundle by showing that an irreducible curve d of degree dr on x d represents the first chern class of a rank r ulrich bundle on x d if and only if the kernel bundle of the general smooth element of d admits a generalized theta divisor moreover we show that any smooth arithmetically gorenstein surface whose ulrich bundles admit such a characterization is necessarily del pezzo this result is applied to produce new examples of complete intersection curves with semistable kernel bundle and also combined with work of farkas musta and popa to relate the existence of ulrich bundles on x d to the minimal resolution conjecture for curves lying on x d in particular we show that a smooth irreducible curve d of degree 3r lying on a smooth cubic surface x 3 represents the first chern class of an ulrich bundle on x 3 if and only if the minimal resolution conjecture holds for the general smooth element of d

schur products and matrix completions we prove that a necessary and sufficient condition for a given partially positive matrix to have a positive completion is that a certain schur product map defined on a certain subspace of matrices is a positive map by analyzing the positive elements of this subspace we obtain new proofs of the results of h dym and i gohberg and grone johnson sa and wolkowitz linear algebra appl 58 1984 109 124 linear algebra appl 36 1981 1 24 we also obtain a new proof of a result of u haagerup decomposition of completely bounded maps on operation algebras preprint characterizing the norm of schur product maps and a new hahn banach type extension theorem for these maps finally we obtain generalizations of many of these results to matrices of operators which we apply to the study of representations of certain subalgebras of the n n matrices

closed convex hulls of unitary orbits in c algebras of real rank zero abstract in this paper we study closed convex hulls of unitary orbits in various c algebras for unital c algebras with real rank zero and a faithful tracial state determining equivalence of projections a notion of majorization describes the closed convex hulls of unitary orbits for self adjoint operators other notions of majorization are examined in these c algebras combining these ideas with the dixmier property we demonstrate unital infinite dimensional c algebras of real rank zero and strict comparison of projections with respect to a faithful tracial state must be simple and have a unique tracial state also closed convex hulls of unitary orbits of self adjoint operators are fully described in unital simple purely infinite c algebras

large elasto plastic finite element analysis of solids and shells with the enhanced assumed strain concept abstract a finite element simulation of arbitrarily large elasto plastic deformations of three dimensional and shell structures is described two numerical aspects originally developed by j c simo have been combined i e the multiplicative large strain plasticity and the enhanced assumed strain finite element concept the constitutive model is worked out in its algorithmic version applying projection methods and consistent linearization the enhanced strain field is added to the conventional hexahedral displacement elements avoiding volumetric locking in the plastic range in addition to solid structures the three dimensional material model without any modifications is also applied to thin walled shell structures here an extended shell formulation a so called seven parameter model is used in which the thickness strain is augmented by a linear term the applicability of the entire formulation is demonstrated by several numerical examples

on the clifford algebra of a binary form the clifford algebra cj of a binary form f of degree d is the k algebra k x y i where i is the ideal generated by ax y d f e k c f has a natural homomorphic image a f that is a rank d 2 azumaya algebra over its center we prove that the center is isomorphic to the coordinate ring of the complement of an explicit divisor in pic d g 1 c where c is the curve w d f u v and g is the genus of c

a model of finite strain viscoplasticity based on unified constitutive equations theoretical and computational considerations with applications to shells abstract a model of multiplicative finite strain viscoplasticity is developed hereby the elastic internal potential is assumed to depend quadratically on the elastic strain measure ce by means of corresponding invariants hence possible extension of the model to take anisotropy into account is straightforward the evolution equation of the unified type due to bodner and partom asme j appl mech 42 1975 385 are modified so as to fit into the framework adopted the numerical treatment of the problem is fully developed specifically the algorithmic aspects of the resulting non additive structure are intensively discussed hereby the treatment of the exponential map of a non symmetric argument is of a central importance two consistent methods are developed various applications to shell problems are considered hereby a shell theory with seven degrees of freedom together with a 4 node enhanced strain finite element formulation are used a central feature of the shell formulation is its eligibility to the application of a three dimensional constitutive law

on azumaya algebras arising from clifford algebras in this paper we continue the investigation begun in haile 4 and tesser 12 into the structure of the clifford algebra of a form if f is a form of degree d in n variables over a field f then the clifford algebra off is the f algebra c r t where r fix x is the free associative f algebra in n variables and t is the ideal generated by a x x y f 1 cx jcxl cl f if d 2 this is the classical clifford algebra of a quadratic form if d 2 then this is also called the generalized clifford algebra and has been studied by various authors see roby 111 revoy lo childs 2 in haile 4 it was shown that if d 3 and n 2 i e iffis a binary cubic form and the characteristic of the field f is not 2 or 3 then the clifford algebra c of the form is azymaya with center the affine coordinate ring of an explicitly given elliptic curve over f the center was also determined by heerema in 6 moreover the algebra c can be extended to an azumaya algebra over the projective closure of the elliptic curve applying the pairing investigated by lichtenbaum 4 and manin 9 one obtains then for each field extension k f a homomorphism from the group of k rational points on the elliptic curve to the brauer group of k given by specialization in lo revoy using results of roby 111 exhibited an explicit f basis for the clifford algebra of an arbitrary form using this basis it is easy to

on a matrix inequality abstract let s n be the set of all n n real symmetric matrices we give a complete characterization of the set of matrix convex functions defined on s n we also consider connections between matrix monotonicity in the lowner sense and matrix convexity

deformation analysis for finite elastic plastic strains in a lagrangean type description abstract a general concept is presented to analyse the deformation of structures undergoing arbitrarily large elastic and arbitrarily large plastic strains based on the multiplicative decomposition of the deformation gradient into elastic and plastic contributions the kinematics of two superposed finite non coaxial deformations are investigated lagrangean type elastic and plastic stretch tensors are introduced and multiplicative decompositions of the total stretch into these elastic and plastic stretches are derived it is shown that the result is independent of any decomposition of the total rotation into an elastic and a plastic rotation for the second superposed deformation the total lagrangean logarithmic hencky strain tensor with corresponding elastic and plastic logarithmic strains is defined if in a large deformation analysis the first deformation is updated such that the second deformation is constrained to be moderately large then the total logarithmic strain tensor of the second deformation can be additively decomposed into purely elastic and purely plastic parts this enables an appropriate formulation of constitutive equations for isotropic hyperelastic material behavior with associated flow rule and evolution laws for combined isotropic kinematic hardening work conjugate to the elastic logarithmic strain tensor is a back rotated kirchhoff stress tensor the rotational change of its reference configuration during the update is given explicitly finally the principle of virtual work with corresponding equilibrium equations and static and geometric boundary conditions is given the virtual work functional is transformed to deliver the consistent tangent stiffness matrix as basis for a finite element solution algorithm

majorization doubly stochastic matrices and comparison of eigenvalues abstract 1 basic properties of majorization 2 isotone maps and algebraic operations 3 double sub and superstochasticity 4 doubly stochastic matrices 5 doubly stochastic matrices with minimum permanent 6 comparison of eigenvalues 7 doubly stochastic maps

analysis of spectral variation and some inequalities a geometric method based on a decomposition of the space of complex matrices is employed to study the variation of the spectrum of a matrix when adapted to special cases this leads to some classical inequalities as well as some new ones as an example of the latter we show that if u v are unitary matrices and k is a skew hermitian matrix such that uv exp k then for every unitary invariant norm the distance between the eigenvalues of v and those of vis bounded by k this generalises two earlier results which used particular unitary invariant norms

the golden thompson trace inequality is complemented we prove a class of trace inequalities which complements the golden thompson inequality for example tr epa epb 2 p tr ea b holds for all p 0 when a and b are hermitian matrices and denotes the geometric mean we also prove related trace inequalities involving the logarithmic function namely p 1tr x log yp 2xpyp 2 tr x log x log y p 1tr x log xp 2ypxp 2 for all p 0 when x and y are nonnegative matrices these inequalities supply lower and upper bounds on the relative entropy

spectral variation of normal matrices abstract it has been a durable conjecture that the distance appropriately defined between the spectra of two normal matrices is bounded by the operator norm of their difference we report on some numerical studies that show that this conjecture is in general false in fact even in the 3 x 3 case the spectral distance may exceed the norm distance by between 1 and 2 percent we also describe the background of the conjecture and offer an analysis of extremal counterexamples

a generalization of the hoffman wielandt theorem abstract the well known inequality of a j hoffman and h w wielandt is extended from single normal operators to commuting tuples of such operators

a characterization of strong preservers of matrix majorization abstract a matrix a is said to be matrix majorized by a matrix b written a b if there exists an n n row stochastic matrix x such that a bx this is a generalization of multivariate majorization in this paper we characterize the linear operators that strongly preserve the matrix majorization

an inequality for hilbert schmidt norm for the absolute value c c c 1 2 and the hilbert schmidt norm c hs trc c 1 2 of an operatorc the following inequality is proved for any bounded linear operatorsa andb on a hilbert space a b hs leqq 2 1 2 a b hs the corresponding inequality for two normal state and of a von neumann algebram is also proved in the following form d varphi psi leqq xi varphi xi psi leqq 2 1 2 d varphi psi here denotes the unique vector representative of a state in a natural positive conep form andd denotes the bures distance defined as the infimum which is also the minimum of the distance of vector representatives of and in particular xi varphi 1 xi varphi 2 leqq 2 1 2 xi 1 xi 2 for any vector representatives j of j j 1 2

on some operator inequalities a real valued continuous function f 2 defined on a finite or infinite interval of the real line is said to be operator monotone if for any pair of bounded selfadjoint operators a b on an infinite dimensional hilbert space a b implies f a f b here f a and f b are defined according to the usual functional calculus and refers to the order relation induced by the cone of positive semi definite operators operator monotony is quite a restrictive condition in fact for p 0 the function f 2 2 p is operator monotone on the half line 0 c if and only if 0 1 the function f 2 2 p possesses some property akin to operator monotony in this direction furuta i 3 recently observed that if r 0 p 0 q 1 satisfies 1 2r q p 2r then a b 0 implies a tp 2 q arbpa r l if p 2r and q 2 the requirement is automatically satisfied hence a p ap 2bpap 2 i 2 whenever a b 0 when a is invertible this means that

some eigenvalue inequalities for positive semidefinite matrix power products abstract we study the eigenvalues of positive semidefinite matrix power products and obtain some inequalities most of which are in terms of majorization in particular for a b 0 0 we prove log 1 a b log 1 a b the result is a generalization of some work of marcus lieb thirring le couteur bushell and trustrum

on an algebra determined by a quartic curve of genus one abstract let k be a field of characteristic not two to each irreducible quartic f x over k we associate a certain algebra a f given by explicit generators and relations we prove a f is an azumaya algebra of rank four over its center and that its center is the coordinate ring of an affine piece of an elliptic curve the jacobian of the curve c y 2 f x its simple images are quaternion algebras and the resulting function from the group of k rational points on the jacobian to the brauer group of k is a group homomorphism whose image is the relative brauer group of central simple k algebra split by the function field of c we also show that the algebra a f is split if and only if c has a k rational point

the nuclear dimension of c algebras abstract we introduce the nuclear dimension of a c algebra this is a noncommutative version of topological covering dimension based on a modification of the earlier concept of decomposition rank our notion behaves well with respect to inductive limits tensor products hereditary subalgebras hence ideals quotients and even extensions it can be computed for many examples in particular it is finite for all uct kirchberg algebras in fact all classes of nuclear c algebras which have so far been successfully classified consist of examples with finite nuclear dimension and it turns out that finite nuclear dimension implies many properties relevant for the classification program surprisingly the concept is also linked to coarse geometry since for a discrete metric space of bounded geometry the nuclear dimension of the associated uniform roe algebra is dominated by the asymptotic dimension of the underlying space

perturbation of spectral subspaces and solution of linear operator equations abstract let a and b be normal operators on a hilbert space let k a and k b be subsets of the complex plane at distance at least from each other let e be the spectral projector for a belonging to k a and let f be the spectral projector for b belonging to k b our main results are estimates of the form ef c e a b f in some special situations the constant c is as low as 1 as an application we prove for an absolute constant d that if the space is finite dimensional and if a and b are normal with a b d then the spectrum of b can be obtained from that of a multiplicities counted by moving each eigenvalue by at most our main results have equivalent formulations as statements about the operator equation aq qb s let a and b be normal operators on perhaps different hilbert spaces assume a k a and b k b where k a k b and are as before then we give estimates of the forms q c aq qb

majorization and singular values iii abstract we obtain a majorization inequality which relates the singular values of a complex square matrix a and those of t a where t is a linear map the inequality takes a particularly simple form if t is positive the results generalize several known majorization inequalities for eigenvalues and singular values

an algebraic approach to the radius of comparison the radius of comparison is an invariant for unital c algebras which extends the theory of covering dimension to noncommutative spaces we extend its definition to general c algebras and give an algebraic as opposed to functional theoretic reformulation this yields new permanence properties for the radius of comparison which strengthen its analogy with covering dimension for commutative spaces we then give several applications of these results new examples of c algebras with finite radius of comparison are given and the question of when the cuntz classes of finitely generated hilbert modules form a hereditary subset of the cuntz semigroup is addressed most interestingly perhaps we treat the question of when a full hereditary subalgebra b of a stable c algebra a is itself stable giving a characterization in terms of the radius of comparison we also use the radius of comparison to quantify the least n for which a c algebra d without bounded 2 quasitraces or unital quotients has the property that mn d is stable

symmetric function means of positive operators abstract many authors have studied means involving ratios of the elementary symmetric functions this work involves generalizing these means to an operator theoretic setting and extending many of the classical scalar inequalities to operators it is shown that these operator means are related to electrical networks

minimax problems on grassmann manifolds sums of eigenvalues courbures principales et energies de hartree fock grassmanniens des domaines de forme quadratique cycles de schubert le plongement de plucker fonctions de morse quadratiques caracterisation minimax de sommes de valeurs propres

majorizations and inequalities in matrix theory abstract in matrix theory majorization plays a significant role for instance majorization relations among eigenvalues and singular values of matrices produce a lot of norm inequalities and even matrix inequalities this survey article is intended as a review of recent results in matrix theory related to majorization

on an algebra associated to a ternary cubic curve abstract in this paper we construct an algebra associated to a cubic curve c defined over a field f of characteristic not two or three we prove that this algebra is an azumaya algebra of rank nine its center is the affine coordinate ring of an elliptic curve the jacobian of the cubic curve c the induced function from the group of f rational points on the jacobian into the brauer group of f is a group homomorphism with image precisely the relative brauer group of classes of central simple f algebras split by the function field of c we also prove that this algebra is split if and only if the cubic curve c has an f rational point these results generalize haile s work on the clifford algebra of a binary cubic form

a note on the hadamard product of matrices it is shown that the smallest eigenvalue of the hadamard product a b of two positive definite hermitian matrices is bounded from below by the smallest eigenvalue of abt

a generalization of spectral radius numerical radius and spectral norm abstract let c n be the linear space of complex column vectors with n coordinates associated with the usual inner product denote by k the set of all k tuples of orthonormal vectors in c n given a real number p 1and an n n complex matrix a with eigenvalues 1 n we define p k max j 1 k i j p 1 p 1 i 1 k n r p k max i 1 k x i ax i p 1 p x 1 x k k and a p k max i 1 k x i ay i p 1 p x 1 x k y 1 y k k as the p k spectral radius p k numerical radius and p k spectral norm of a respectively for k 1 they are the classical spectral radius numerical radius and spectral norm of a in this note we study the matrices for which p k a rp k a p k a a p k or rp k a a p k moreover the norm properties of rp k and p k are investigated

on permutations convex hulls and normal operators abstract a spectral characterization is obtained for those normal operators which belong to the convex hull of the unitary orbit of a given normal operator on a finite dimensional space this is used to prove the following if a and b are normal operators on an n dimensional complex hilbert space h with eigenvalues given by 1 n and 1 n respectively and if a b is also normal then a b max s n diag k k for any unitarily invariant norm on l h

necessary and sufficient conditions for multivariate majorization abstract let x and y be m n matrices whose elements are in k a real or complex field we obtain necessary and sufficient conditions for the existence of a matrix a belonging to the convex hull of a certain subgroup of the general linear group gl n k such that x ya which unite and generalize several known results concerning majorization

the relationship between hadamard and conventional multiplication for positive definite matrices abstract it is known that if a is positive definite hermitian then a a 1 i in the positive semidefinite ordering our principal new result is a converse to this inequality under certain weak regularity assumptions about a function f on the positive definite matrices a f a af a for all positive definite a if and only if f a is a positive multiple of a 1 in addition to the inequality a a 1 i it is known that a a 1 t i and stronger that min a b min ab t for a b positive definite hermitian we also show that min a b min ab and note that min ab and min ab t can be quite different for a b positive definite hermitian we utilize a simple technique for dealing with the hadamard product which relates it to the conventional product and which allows us to give especially simple proofs of the closure of the positive definites under hadamard multiplication and of the inequalities mentioned

on majorization and schur products abstract suppose a d1 dm are n n matrices where a is self adjoint and let x m k 1 d k ad k it is shown that if d k d k d k d k i then the spectrum of x is majorized by the spectrum of a in general without assuming any condition on d1 dm a result is obtained in terms of weak majorization if each dk is a diagonal matrix then x is equal to the schur entrywise product of a with a positive semidefinite matrix thus the results are applicable to spectra of schur products of positive semidefinite matrices if a b are self adjoint with b positive semidefinite and if bii 1 for each i it follows that the spectrum of the schur product of a and b is majorized by that of a a stronger version of a conjecture due to marshall and olkin is also proved

non commutative banach function spaces in this paper we survey some aspects of the theory of non commutative banach function spaces that is spaces of measurable operators associated with a semi finite von neumann algebra these spaces are also known as non commutative symmetric spaces the theory of such spaces emerged as a common generalization of the theory of classical commutative rearrangement invariant banach function spaces in the sense of w a j luxemburg and a c zaanen and of the theory of symmetrically normed ideals of bounded linear operators in hilbert space in the sense of i c gohberg and m g krein these two cases may be considered as the two extremes of the theory in the first case the underlying von neumann algebra is the commutative algebra l on some measure space with integration as trace in the second case the underlying von neumann algebra is b the algebra of all bounded linear operators on a hilbert space with standard trace important special cases of these non commutative spaces are the non commutative l p spaces which correspond in the commutative case with the usual l p spaces on a measure space and in the setting of symmetrically normed operator ideals they correspond to the schatten p classes mathfrak s p

a theoretical and computational model for isotropic elastoplastic stress analysis in shells at large strains the article presents new aspects of large strain isotropic elastoplastic analysis of shells on the shell theory side we consider several possible continuum based parametrizations of the shell deformation and investigate their applicability with respect to the implementation of general three dimensional local constitutive models as an aspect of computational shell analysis we then discuss in detail the numerical implementation of a shell based on the parametrization of the top and bottom surface in terms of a new 8 node brick type mixed finite shell element on the basis of assumed strain and enhanced strain variational approaches on the side of plasticity theory we adopt a recently proposed intermediate configuration free formulation of large strain plasticity based on the notion of a plastic metric and consider its representation with respect to the parameter manifold of the shell this frame is formulated in terms of principal strains and principal stresses with respect to dual co and contra variant eigenvector triads associated with a mixed variant elastic strain tensor the new aspect of computational plasticity is the development of a stress update algorithm for the plasticity model mentioned above which includes a general return mapping in the eigenvalue space the algorithm can be applied to general coordinate charts and is particularly convenient when formulated with respect to the space of the curvilinear coordinates of the shell parametrization we demonstrate the performance of the finite element formulation and constitutive algorithms by means of several numerical examples

log majorization and complementary golden thompson type inequalities abstract we obtain a log majorization result for power means of positive semidefinite matrices this implies matrix norm inequalities for unitarily invariant norms which are considered as complementary to the golden thompson one other log majorization results are also obtained we give logarithmic trace inequalities and determinant inequalities as applications of our log majorizations

inequalities for the schatten p norm iv we present some inequalities for the schattenp norm of operators on a hilbert space it is shown among other things that ifa is an operator such that rea a 0 then for any operatorx ax xa p 2a x p also for any two operatorsa andb a b 2 2 a b 2 2 2 a b 2 2

three dimensional extension of non linear shell formulation based on the enhanced assumed strain concept conventional shell formulations such as 3 or 5 parameter theories or even 6 parameter theories including the thickness change as extra parameter require a condensation of the constitutive law in order to avoid a significant error due to the assumption of a linear displacement field across the thickness this means that the normal stress in thickness direction has to either vanish or be constant in general these extra constraints cannot be satisfied explicitly or they lead to elaborate strain expressions the main objective of the present study is to introduce directly a complete 3 d constitutive law without modification therefore a 7 parameter theory is utilized which includes a linear varying thickness stretch as extra variable allowing also large strain effects

a note on the hoffman wielandt theorem an elementary proof of a recent generalization of the hoffman wielandt theorem to commuting m tuples of normal matrices by bhatia and bhattacharyya is given in the case m 1 this provides a derivation which though using the same tools avoids some unnecessary calculations and is thus shorter than the original one and that to be found in the standard literature

central sequence c algebras and tensorial absorption of the jiang su algebra we study properties of the central sequence algebra a a 0 of a c algebra a and we present an alternative approach to a recent result of matui and sato they prove that every unital separable simple nuclear c algebra whose trace simplex is nite dimensional tensorially absorbs the jiang su algebra if and only if it has the strict comparison property we extend their result to the case where the extreme boundary of the trace simplex is closed and of nite topological dimension we are also able to relax the assumption on the c algebra of having the strict com parison property to a weaker property that we call local weak comparison namely we prove that a unital separable simple nuclear c algebra whose trace simplex has nite dimensional closed extreme boundary tensorially absorbs the jiang su algebra if and only if it has the local weak comparison property we can also eliminate the nuclearity assumption if instead we assume the si property of matui and sato and moreover that each ii1 factor representation of the c algebra is a mcdu factor

a note on the arithmetic geometric mean inequality for matrices abstract we give a simple proof of the inequality aa x xbb 2 a ab where a b and x are arbitrary n n matrices and is any unitarily invariant norm for the schatten p norms p with 1 p aa x xbb p 2 a xb p if and only if aa x xbb