arveson s criterion for unitary similarity abstract this paper is an exposition of w b arveson s complete invariant for the unitary similarity of complex irreducible matrices

convergence of the new composite implicit iteration process with random errors abstract in this paper strong convergence theorems for approximation of common fixed points of a finite family of asymptotically demicontractive mappings are proved in banach spaces using the new composite implicit iteration scheme with errors our results of this paper improve and extend the corresponding results of chen song zhou r d chen y s song h y zhou convergence theorems for implicit iteration process for a finite family of continuous pseudocontractive mappings j math anal appl 314 2006 701 709 osilike m o osilike implicit iteration process for common fixed points of a finite family of strictly pseudocontractive maps j math anal appl 294 2004 73 81 gu f gu the new composite implicit iterative process with errors for common fixed points of a finite family of strictly pseudocontractive mappings j math anal appl 329 2007 766 776 and yang and hu l p yang g hu convergence of implicit iteration process with random errors acta math sinica chin ser 51 1 2008 11 22

periodic solutions of a periodic lotka volterra system with delays a lotka volterra periodic delay model with m predators and n preys is studied in this paper sufficient conditions for the global existence of a positive periodic solutions of this delay model are obtained by means of topological degree finally a suitable example is given to illustrate that the conditions of the main theorem are feasible

implicit iteration process for common fixed points of a finite family of strictly pseudocontractive maps convergence theorems for approximation of common fixed points of strictly pseudocontractive mappings of browder petryshyn type are proved in banach spaces using an implicit iteration scheme recently introduced by xu and ori numer funct anal optim 22 2001 767 773

composite implicit iteration process for common fixed points of a finite family of strictly pseudocontractive maps abstract let e be a real banach space and let k be a nonempty closed convex subset of e let t i i 1 n be n strictly pseudocontractive self maps of k such that f i 1 n f t i where f t i x k t i x x and let n n 1 n n 1 0 1 be two real sequence satisfying the conditions i n 1 1 n ii n 1 1 n 2 iii n 1 1 n iv 1 n 1 n l 2 1 n 1 where l 1 is common lipschitz constant of t i i 1 n for x 0 k let x n n 1 be new implicit process defined by x n n x n 1 1 n t n y n y n n x n 1 1 n t n x n where t n t n mod n then i lim n x n p exists for all p f ii lim inf n x n t n x n 0 the results of this paper generalize and improve the results of osilike in 2004 in this paper the proof methods of the main results are also different from that of osilike

matrix poincare φ sobolev inequalities and quantum ensembles sobolev type inequalities have been extensively studied in the frameworks of real valued functions and non commutative lp spaces and have proven useful in bounding the time evolution of classical quantum markov processes among many other applications in this paper we consider yet another fundamental setting matrix valued functions and prove new sobolev type inequalities for them our technical contributions are two fold i we establish a series of matrix poincare inequalities for separably convex functions and general functions with gaussian unitary ensembles inputs and ii we derive sobolev inequalities for matrix valued functions defined on boolean hypercubes and for those with gaussian distributions our results recover the corresponding classical inequalities i e real valued functions when the matrix has one dimension finally as an application of our technical outcomes we derive the upper bounds for a fundamental entropic quantity the holevo quantity in quantum information science since classical quantum channels are a special instance of matrix valued functions this is obtained through the equivalence between the constants in the strong data processing inequality and the sobolev inequality

jensen s inequality for spectral order and submajorization abstract let a be a c algebra and a l h be a positive unital map then for a convex function f i r defined on some open interval and a self adjoint element a a whose spectrum lies in i we obtain a jensen s type inequality f a f a where denotes an operator preorder usual order spectral preorder majorization and depends on the class of convex functions considered i e monotone convex or arbitrary convex functions some extensions of jensen s type inequalities to the multi variable case are considered

on projection algorithms for solving convex feasibility problems due to their extraordinary utility and broad applicability in many areas of classical mathematics and modern physical sciences most notably computerized tomography algorithms for solving convex feasibility problems continue to receive great attention to unify generalize and review some of these algorithms a very broad and flexible framework is investigated several crucial new concepts which allow a systematic discussion of questions on behaviour in general hilbert spaces and on the quality of convergence are brought out numerous examples are given

spectra and variance of quantum random variables abstract we study essentially bounded quantum random variables and show that the gelfand spectrum of such a quantum random variable coincides with the hypoconvex hull of the essential range of moreover a notion of operator valued variance is introduced leading to a formulation of the moment problem in the context of quantum probability spaces in terms of operator theoretic properties involving semi invariant subspaces and spectral theory as an application of quantum variance new measures of random and inherent quantum noise are introduced for measurements of quantum systems modifying some recent ideas of polterovich 17

strong convergence theorems for finitely many nonexpansive mappings and applications abstract let e be a uniformly convex banach space which satisfies opial s condition or whose norm is frechet differentiable recently takahashi and shimoji w takahashi k shimoji convergence theorems for nonexpansive mappings and feasibility problems math comput modelling 32 2000 1463 1471 introduced an iterative scheme given by finitely many nonexpansive mappings in e and proved weak convergence theorems which are connected with the problem of image recovery in this paper we introduce a new iterative scheme which includes their iterative scheme as a special case under the assumption that e is a reflexive banach space whose norm is uniformly g teaux differentiable and which has a weakly continuous duality mapping we prove strong convergence theorems which are connected with the problem of image recovery using the established results we consider the problem of finding a common fixed point of finitely many nonexpansive mappings

characterizations of matrix and operator valued φ entropies and operator efron stein inequalities we derive new characterizations of the matrix entropy functionals introduced in chen tropp chen tropp 2014 electron j prob 19 1 30 doi 10 1214 ejp v19 2964 1 these characterizations help us to better understand the properties of matrix entropies and are a powerful tool for establishing matrix concentration inequalities for random matrices then we propose an operator valued generalization of matrix entropy functionals and prove the subadditivity under lowner partial ordering our results demonstrate that the subadditivity of operator valued entropies is equivalent to the convexity as an application we derive the operator efron stein inequality 1 http dx doi org 10 1214 ejp v19 2964

isometries of the toeplitz matrix algebra abstract we study the structure of isometries defined on the algebra a of upper triangular toeplitz matrices our first result is that a continuous multiplicative norm preserving map a m n c must be of the form either a u a u or a u a u where a is the complex conjugation and u is a unitary matrix in our second result we use a range of ideas in operator theory and linear algebra to show that every linear isometry a m n c is of the form a u a v where u and v are two unitary matrices this implies in particular that every such an isometry is a complete isometry and that a unital linear isometry a m n c is necessarily an algebra homomorphism

inconsistent signal feasibility problems least squares solutions in a product space presents parallel projection methods to find least squares solutions to inconsistent convex set theoretic signal synthesis problems the problem of finding a signal that minimizes a weighted average of the squares of the distances to constraint sets is reformulated in a product space where it is equivalent to that of finding a point that lies in a particular subspace and at minimum distance from the cartesian product of the original sets a solution is obtained in the product space via methods of alternating projections which naturally lead to methods of parallel projections in the original space the convergence properties of the proposed methods are analyzed and signal synthesis applications are demonstrated

permanence of a delayed non autonomous gilpin ayala competition model abstract in this paper we consider a delayed non autonomous n species gilpin ayala competitive system which is more general and more realistic then classical lotka volterra competition model by means of ahmad and lazer s definitions of lower and upper averages of a function we give the average conditions for the permanence of the system it is shown that our result is the generalization of those of zhao et al j d zhao j f jiang a c lazer the permanence and global attractivity in a nonautonomous lotka volterra system nonlinear analysis real world applications 5 4 2004 265 276 our results also supplement the results of fan and wang m fan k wang global periodic solutions of a generalized n species gilpin ayala competition model computer and mathematics with applications 40 2000 1141 1151

the new composite implicit iterative process with errors for common fixed points of a finite family of strictly pseudocontractive mappings abstract convergence theorems for approximation of common fixed points of strictly pseudocontractive mappings of browder petryshyn type are proved in banach spaces using a new composite implicit iteration scheme with errors the results presented in this paper generalize and improve the corresponding results of m o osilike m o osilike implicit iteration process for common fixed points of a finite family of strictly pseudocontractive maps j math anal appl 294 2004 73 81

effective results on compositions of nonexpansive mappings abstract this paper provides uniform bounds on the asymptotic regularity for iterations associated to a finite family of nonexpansive mappings we obtain our quantitative results in the setting of r convex spaces a class of geodesic spaces which generalizes metric spaces with a convex geodesic bicombing

on the convergence of implicit iteration process with error for a finite family of asymptotically nonexpansive mappings abstract the purpose of this paper is to study the weak and strong convergence of implicit iteration process with errors to a common fixed point for a finite family of asymptotically nonexpansive mappings and nonexpansive mappings in banach spaces the results presented in this paper extend and improve the corresponding results of h bauschke the approximation of fixed points of compositions of nonexpansive mappings in hilbert space j math anal appl 202 1996 150 159 b halpern fixed points of nonexpansive maps bull amer math soc 73 1967 957 961 p l lions approximation de points fixes de contractions c r acad sci paris ser a 284 1977 1357 1359 s reich strong convergence theorems for resolvents of accretive operators in banach spaces j math anal appl 75 1980 287 292 z h sun strong convergence of an implicit iteration process for a finite family of asymptotically quasi nonexpansive mappings j math anal appl 286 2003 351 358 r wittmann approximation of fixed points of nonexpansive mappings arch math 58 1992 486 491 h k xu m g ori an implicit iterative process for nonexpansive mappings numer funct anal optimiz 22 2001 767 773 y y zhou s s chang convergence of implicit iterative process for a finite family of asymptotically nonexpansive mappings in banach spaces numer funct anal optimiz 23 2002 911 921

strong convergence of an implicit iteration process for a finite family of asymptotically quasi nonexpansive mappings in the present paper we prove that the modified implicit iteration sequence for a finite family of asymptotically quasi nonexpansive mappings converges strongly to a common fixed point of the family in a uniformly convex banach space requiring one member t in the family to be semi compact our results extend and improve some recent results

hopf bifurcation and global stability for a delayed predator prey system with stage structure for predator abstract in this paper a delayed predator prey system with stage structure for predator is proposed and studied it is found that the time delay is harmless for permanence of the stage structured system if 1 we show that the unique positive equilibrium is locally asymptotically stable when time delay is sufficiently small while loss of stability by a hopf bifurcation can occur as the delay increases

a criterion for unitary similarity of upper triangular matrices in general position abstract each square complex matrix is unitarily similar to an upper triangular matrix with diagonal entries in any prescribed order let a a ij and b b ij be upper triangular n n matrices that are not similar to direct sums of square matrices of smaller sizes or are in general position and have the same main diagonal we prove that a and b are unitarily similar if and only if h a k h b k for all h c x and k 1 n where a k a ij i j 1 k and b k b ij i j 1 k are the leading principal k k submatrices of a and b and is the frobenius norm

conditional expectation and bayes rule for quantum random variables and positive operator valued measures a quantum probability measure is a function on a algebra of subsets of a locally compact and hausdorff sample space that satisfies the formal requirements for a measure but where the values of are positive operators acting on a complex hilbert space and a quantum random variable is a measurable operator valued function although quantum probability measures and random variables are used extensively in quantum mechanics some of the fundamental probabilistic features of these structures remain to be determined in this paper we take a step toward a better mathematical understanding of quantum random variables and quantum probability measures by introducing a quantum analogue for the expected value e of a quantum random variable relative to a quantum probability measure in so doing we are led to theorems for a change of quantum measure and a change of quantum variables we also introduce a quantum conditional expectation which results in quantum versions of some standard identities for r

regularized and inertial algorithms for common fixed points of nonlinear operators this paper deals with a general fixed point iteration for computing a point in some nonempty closed and convex solution set included in the common fixed point set of a sequence of mappings on a real hilbert space the proposed method combines two strategies viscosity approximations regularization and inertial type extrapolation the first strategy is known to ensure the strong convergence of some successive approximation methods while the second one is intended to speed up the convergence process under classical conditions on the operators and the parameters we prove that the sequence of iterates generated by our scheme converges strongly to the element of minimal norm in the solution set this algorithm works for instance for approximating common fixed points of infinite families of demicontractive mappings including the classes of quasi nonexpansive operators and strictly pseudocontractive ones

the shilov boundary of an operator space and the characterization theorems abstract we study operator spaces operator algebras and operator modules from the point of view of the noncommutative shilov boundary in this attempt to utilize some noncommutative choquet theory we find that hilbert c modules and their properties which we studied earlier in the operator space framework replace certain topological tools we introduce certain multiplier operator algebras and c algebras of an operator space which generalize the algebras of adjointable operators on a c module and the imprimitivity c algebra it also generalizes a classical banach space notion this multiplier algebra plays a key role here as applications of this perspective we unify and strengthen several theorems characterizing operator algebras and modules we also include some general notes on the commutative case of some of the topics we discuss coming in part from joint work with christian le merdy about function modules

permanence of a nonlinear prey competition model with delays abstract a nonlinear periodic predator prey model with m preys and n m predators and delays is studied which can be seen as the modification of the traditional lotka volterra prey competition model two sets of sufficient conditions which guarantee the permanence of the system are obtained one set is delay independent while the other set is delay dependent our results supplement those obtained by chen et al f d chen x d xie j l shi existence uniqueness and stability of positive periodic solution for a nonlinear prey competition model with delays journal of computational and applied mathematics 194 2 2006 368 387

existence uniqueness and stability of positive periodic solution for a nonlinear prey competition model with delays a nonlinear periodic predator prey model with m preys and n m predators and delays is proposed in this paper which can be seen as the modification of the traditional lotka volterra prey competition model sufficient conditions which guarantee the existence of a unique globally attractive positive periodic solution of the system are obtained

steered sequential projections for the inconsistent convex feasibility problem we study a steered sequential gradient algorithm which minimizes the sum of convex functions by proceeding cyclically in the directions of the negative gradients of the functions and using steered step sizes this algorithm is applied to the convex feasibility problem by minimizing a proximity function which measures the sum of the bregman distances to the members of the family of convex sets the resulting algorithm is a new steered sequential bregman projection method

jensen s inequality relative to matrix valued measures a bochner integral formulation of jensen s inequality is presented for hermitian matrix valued functions and measures

the approximation of fixed points of compositions of nonexpansive mappings in hilbert space determining fixed points of nonexpansive mappings is a frequent problem in mathematics and physical sciences an algorithm for finding common fixed points of nonexpansive mappings in hilbert space essentially due to halpern is analyzed the main theorem extends wittmann s recent work and partially generalizes a result by lions algorithms of this kind have been applied to the convex feasibility problem

positive periodic solutions of a class of delay differential system with feedback control with the help of continuation theorem based on gaines and mawhin s coincidence degree sufficient and realistic conditions are obtained for the global existence of positive periodic solutions for the delay differential system with feedback control when these results are applied to some special delay population models some new results are obtained and some known results are generalized

a general iterative method for a finite family of nonexpansive mappings abstract we study the approximation of common fixed points of a finite family of nonexpansive mappings and suggest a modification of the iterative algorithm without the assumption of any type of commutativity also we show that the convergence of the proposed algorithm can be proved under some types of control conditions

convergence theorems for implicit iteration process for a finite family of continuous pseudocontractive mappings abstract in this paper a necessary and sufficient conditions for the strong convergence to a common fixed point of a finite family of continuous pseudocontractive mappings are proved in an arbitrary real banach space using an implicit iteration scheme recently introduced by xu and ori h k xu r g ori an implicit iteration process for nonexpansive mappings numer fuct anal optim 22 2001 767 773 in condition n 0 1 and also strong and weak convergence theorem of a finite family of strictly pseudocontractive mappings of browder petryshyn type is obtained the results presented extend and improve the corresponding results of m o osilike m o osilike implicit iteration process for common fixed points of a finite family of strictly pseudocontractive maps j math anal appl 294 2004 73 81

an operator valued lyapunov theorem abstract we generalize lyapunov s convexity theorem for classical scalar valued measures to quantum operator valued measures in particular we show that the range of a nonatomic quantum probability measure is a weak closed convex set of quantum effects positive operators bounded above by the identity operator under a sufficient condition on the non injectivity of integration to prove the operator valued version of lyapunov s theorem we must first define the notions of essentially bounded essential support and essential range for quantum random variables borel measurable functions from a set to the bounded linear operators acting on a hilbert space

dynamic behaviors of a delay differential equation model of plankton allelopathy in this paper we consider a modified delay differential equation model of the growth of n species of plankton having competitive and allelopathic effects on each other we first obtain the sufficient conditions which guarantee the permanence of the system as a corollary for periodic case we obtain a set of delay dependent condition which ensures the existence of at least one positive periodic solution of the system after that by means of a suitable lyapunov functional sufficient conditions are derived for the global attractivity of the system for the two dimensional case under some suitable assumptions we prove that one of the components will be driven to extinction while the other will stabilize at a certain solution of a logistic equation examples show the feasibility of the main results

a survey of canonical forms and invariants for unitary similarity abstract matrices a and b are said to be unitarily similar if u au b for some unitary matrix u this expository paper surveys results on canonical forms and invariants for unitary similarity the first half gives a detailed description of methods developed by several authors brenner littlewood mitchell mcrae radjavi serge chuk and benedetti and cragnolini using inductively defined reduction procedures to transform matrices to canonical form the matrix is partitioned and successive unitary similarities applied to reduce the submatrices to some nice form at each stage one refines the partition and restricts the set of permissible unitary similarities to those that preserve the already reduced blocks the process ends in a finite number of steps producing both the canonical form and the subgroup of the unitary group that preserves that form depending on the initial step various canonical forms may be defined the method can also be used to define canonical forms relative to certain subgroups of the unitary group and canonical forms for finite sets of matrices under simultaneous unitary similarity the remainder of the paper surveys results on unitary invariants and other topics related to unitary similarity such as the specht pearcy trace invariants the numerical range and unitary reducibility

the capacity of hybrid quantum memory the general stable quantum memory unit is a hybrid consisting of a classical digit with a quantum digit qudit assigned to each classical state the shape of the memory is the vector of sizes of these qudits which may differ we determine when n copies of a quantum memory spl ascr embed in n 1 spl ogr 1 copies of another quantum memory spl bscr this relationship captures the notion that spl bscr is as at least as useful as spl ascr for all purposes in the bulk limit we show that the embeddings exist if and only if for all p spl ges 1 the p norm of the shape of spl ascr does not exceed the p norm of the shape of spl bscr the log of the p norm of the shape of spl ascr can be interpreted as the maximum of s spl rho h spl rho p quantum entropy plus discounted classical entropy taken over all mixed states spl rho on spl ascr we also establish a noiseless coding theorem that justifies these entropies the noiseless coding theorem and the bulk embedding theorem together say that either spl ascr blindly bulk encodes into spl bscr with perfect fidelity or a admits a state that does not visibly bulk encode into spl bscr with high fidelity in conclusion the utility of a hybrid quantum memory is determined by its simultaneous capacity for classical and quantum entropy which is not a finite list of numbers but rather a convex region in the classical quantum entropy plane

specht s criterion for systems of linear mappings abstract w specht 1940 proved that two n n complex matrices a and b are unitarily similar if and only if trace w a a trace w b b for every word w x y in two noncommuting variables we extend his criterion and its generalizations by n a wiegmann 1961 and n jing 2015 to an arbitrary system a consisting of complex or real inner product spaces and linear mappings among them we represent such a system by the directed graph q a whose vertices are inner product spaces and arrows are linear mappings denote by q a the directed graph obtained by enlarging to q a the adjoint linear mappings we prove that a system a is transformed by isometries of its spaces to a system b if and only if the traces of all closed directed walks in q a and q b coincide