convexity of quasi entropy type functions lieb s and ando s convexity theorems revisited given a positive function f on 0 and a non zero real parameter we consider a function if a b x tr x f larb 1 rb x in three matrices a b 0 and x this generalizes the notion of monotone metrics on positive definite matrices and in the literature 1 has been typical we investigate how operator monotony of f is sufficient and or necessary for joint convexity concavity of if a b x similar discussions are given for quasi entropies and quantum skew informations

pullback and pushout constructions in c algebra theory abstract a systematic study of pullback and pushout diagrams is conducted in order to understand restricted direct sums and amalgamated free products of c algebras particular emphasis is given to the relations with tensor products both with the minimal and the maximal c tensor norm thus it is shown that pullback and pushout diagrams are stable under tensoring with a fixed algebra and stable under crossed products with a fixed group general tensor products between diagrams are also investigated the relations between the theory of extensions and pullback and pushout diagrams are explored in some detail the crowning result is that if three short exact sequences of c algebras are given with appropriate morphisms between the sequences allowing for pullback or pushout constructions at the levels of ideals algebras and quotients then the three new c algebras will again form a short exact sequence under some mild extra conditions as a generalization of a theorem of t a loring it is shown that each morphism between a pair of c algebras combined with its extension to the stabilized algebras gives rise to a pushout diagram this result has applications to corona extendibility and conditional projectivity finally the pullback and pushout constructions are applied to the class of noncommutative cw complexes defined by s eilers t a loring and g k pedersen j reine angew math 1998 499 101 143 to show that this category is stable under tensor products and under restricted direct sums

optimal harvesting in predator prey systems we study the harvesting of predators in a predator prey system as an optimal control problem with the goal of maximizing the long term average yield we show that the maximum yield can not be greater than the largest constant rate harvest for which the system has an equilibrium provided the controlled system tends to an equilibrium or has a periodic solution we also give some examples indicating practical strategies using either bang bang or instantaneous harvests whose yields approach this maximum

on a non commutative analogue of a classical result of namioka and phelps abstract a classical result of namioka and phelps states that the square is a test object to verify semi simplexity in the tensor theory of convex compact sets by using the quantization of generalized namioka phelps test spaces we formulate a nuclearity criterion for c algebras which establishes a non commutative version of their result the proof we suggest covers the nuclearity characterization via non commutative polyhedron outlined by effros 8 several matrix systems studied by farenick and paulsen 13 are shown to be test systems for nuclearity we also prove that the standard namioka phelps test space is c nuclear we propose a partition of unity property for c algebras which distinguishes nuclear c algebras among the others

α z renyi relative entropies we consider a two parameter family of renyi relative entropies d z that are quantum generalisations of the classical renyi divergence d p q this family includes many known relative entropies or divergences such as the quantum relative entropy the recently defined quantum renyi divergences as well as the quantum renyi relative entropies all its members satisfy the quantum generalizations of renyi s axioms for a divergence we consider the range of the parameters z for which the data processing inequality holds we also investigate a variety of limiting cases for the two parameters obtaining explicit formulas for each one of them

existence and global stability of periodic solutions of a discrete ratio dependent food chain model with delay by using the continuation theorem base on gaines and mawhin s coincidence degree sufficient and realistic conditions are obtained for the global existence of positive periodic solutions for a discrete time nonautonomous food chain model and sufficient conditions for the global stability of positive periodic solutions are also obtained some known results are extended

ultraproducts of von neumann algebras abstract we study several notions of ultraproducts of von neumann algebras from a unified viewpoint in particular we show that for a sigma finite von neumann algebra m the ultraproduct m introduced by ocneanu is a corner of the ultraproduct m introduced by groh and raynaud using this connection we show that the ultraproduct action of the modular automorphism group of a normal faithful state of m on the ocneanu ultraproduct is the modular automorphism group of the ultrapower state t t applying these results we obtain several properties of the ocneanu ultraproduct of type iii factors which are not present in the tracial ultraproducts for instance it turns out that the ultrapower m of a type iii0 factor is never a factor moreover we settle in the affirmative a recent problem by ueda about the connection between the relative commutant of m in m and connes asymptotic centralizer algebra m

stage structured control on a class of predator prey system in almost periodic environment in this paper we consider a kind of stage structured predator prey systems with two predators and general functional responses by applying the comparison theorem lyapunov functional and mawhin s

jensen s inequality for operators without operator convexity we give jensen s inequality for n tuples of self adjoint operators unital n tuples of positive linear mappings and real valued continuous convex functions with conditions on the bounds of the operators we also study operator quasi arithmetic means under the same conditions

a new application of random matrices ext c _ mathrm red f_2 is not a group in the process of developing the theory of free probability and free entropy voiculescu introduced in 1991 a random matrix model for a free semicircular system since then random matrices have played a key role in von neumann algebra theory cf v8 v9 the main result of this paper is the following extension of voiculescui s random matrix result let x n 1 x n r be a system of r stochastically independent n i n gaussian self adjoint random matrices as in voiculescui s random matrix paper v4 and let x1 xr be a semi circular system in a c probability space then for every polynomial p in r noncommuting variables lim niaeia p x n 1 o x n r o p x1 xr for almost all o in the underlying probability space we use the result to show that the ext invariant for the reduced c algebra of the free group on 2 generators is not a group but only a semi group this problem has been open since anderson in 1978 found the first example of a c algebra a for which ext a is not a group

on joint convexity of trace functions abstract we give the necessary and sufficient condition of the trace function f a b tr a p b q is jointly convex in a b

periodic solutions for delay differential equations model of plankton allelopathy abstract in this paper we propose a modified delay differential equation model of the growth of two species of plankton having competitive and allelopathic effects on each other by using the continuation theorem of coincidence degree theory a set of easily verifiable sufficient conditions are obtained for the existence of positive periodic solutions for this model

higher order extension of lowner s theory operator k tone functions the new notion of operator matrix k tone functions is introduced which is a higher order extension of operator matrix monotone and convex functions differential properties of matrix k tone functions are shown characterizations properties and examples of operator k tone functions are presented in particular integral representations of operator k tone functions are given generalizing familiar representations of operator monotone and convex functions

operator system structures on ordered spaces given an archimedean order unit space v v e we construct a minimal operator system omin v and a maximal operator system omax v which are the analogues of the minimal and maximal operator spaces of a normed space we develop some of the key properties of these operator systems and make some progress on characterizing when an operator system s is completely boundedly isomorphic to either omin s or to omax s we then apply these concepts to the study of entanglement breaking maps we prove that for matrix algebras a linear map is completely positive from omin mn to omax mm if and only if it is entanglement breaking

connes embedding problem and tsirelson s problem we show that tsirelson s problem concerning the set of quantum correlations and connes embedding problem on finite approximations in von neumann algebras known to be equivalent to kirchberg s qwep conjecture are essentially equivalent specifically tsirelson s problem asks whether the set of bipartite quantum correlations generated between tensor product separated systems is the same as the set of correlations between commuting c algebras connes embedding problem asks whether any separable ii1 factor is a subfactor of the ultrapower of the hyperfinite ii1 factor we show that an affirmative answer to connes question implies a positive answer to tsirelson s conversely a positive answer to a matrix valued version of tsirelson s problem implies a positive one to connes problem

on kirchberg s embedding problem kirchberg s embedding problem kep asks whether every separable c algebra embeds into an ultrapower of the cuntz algebra o 2 o 2 in this paper we use model theory to show that this conjecture is equivalent to a local approximate nuclearity condition that we call the existence of good nuclear witnesses in order to prove this result we study general properties of existentially closed c algebras along the way we establish a connection between existentially closed c algebras the weak expectation property of lance and the local lifting property of kirchberg the paper concludes with a discussion of the model theory of o 2 o 2 several results in this last section are proven using some technical results concerning tubular embeddings a notion first introduced by jung for studying embeddings of tracial von neumann algebras into the ultrapower of the hyperfinite ii 1 factor

operator systems from discrete groups we express various sets of quantum correlations studied in the theoretical physics literature in terms of different tensor products of operator systems of discrete groups we thus recover earlier results of tsirelson and formulate a new approach for the study of quantum correlations to do this we formulate a general framework for the study of operator systems arising from discrete groups we study in detail the operator system of the free group mathbb f n on n generators as well as the operator systems of the free products of finitely many copies of the two element group mathbb z 2 we examine various tensor products of group operator systems including the minimal the maximal and the commuting tensor products we introduce a new tensor product in the category of operator systems and formulate necessary and sufficient conditions for its equality to the commuting tensor product in the case of group operator systems

quotients exactness and nuclearity in the operator system category abstract we continue our study of tensor products in the operator system category we define operator system quotients and exactness in this setting and refine the notion of nuclearity by studying operator systems that preserve various pairs of tensor products one of our main goals is to relate these refinements of nuclearity to the kirchberg conjecture in particular we prove that the kirchberg conjecture is equivalent to the statement that every operator system that is min er nuclear is also el c nuclear we show that operator system quotients are not always equal to the corresponding operator space quotients and then study exactness of various operator system tensor products for the operator system quotient we prove that an operator system is exact for the min tensor product if and only if it is min el nuclear we give many characterizations of operator systems that are min er nuclear el c nuclear min el nuclear and el max nuclear these characterizations involve operator system analogues of various properties from the theory of c algebras and operator spaces including the wep and llp

on exotic group c algebras abstract let be a discrete group a c algebra a is an exotic c algebra associated to if there exist proper surjective c quotients c a c r which compose to the canonical quotient c c r in this paper we show that a large class of exotic c algebras has poor local properties more precisely we demonstrate the failure of local reflexivity exactness and local lifting property additionally a does not admit an amenable trace and hence is not quasidiagonal and does not have the wep when a is from the class of exotic c algebras defined by brown and guentner see 8 in order to achieve the main results of this paper we prove a result which implies the factorization property for the class of discrete groups which are algebraic subgroups of locally compact amenable groups

noncommutative l p spaces without the completely bounded approximation property for any 1 leq p leq infty different from 2 we give examples of non commutative lp spaces without the completely bounded approximation property let f be a non archimedian local field if p 4 or p 4 3 and r geq 3 these examples are the non commutative lp spaces of the von neumann algebra of lattices in sl r f or in sl r r for other values of p the examples are the non commutative lp spaces of the von neumann algebra of lattices in sl r f for r large enough depending on p we also prove that if r geq 3 lattices in sl r f or sl r r do not have the approximation property of haagerup and kraus this provides examples of exact c algebras without the operator space approximation property

concavity of the auxiliary function for classical quantum channels the auxiliary function of a classical channel appears in two fundamental quantities the random coding exponent and the sphere packing exponent which yield upper and lower bounds on the error probability of decoding respectively a crucial property of the auxiliary function is its concavity and this property consequently leads to several important results in finite blocklength analysis in this paper we prove that the auxiliary function of a classical quantum channel also enjoys the same concavity property extending an earlier partial result to its full generality we also prove that the auxiliary function satisfies the data processing inequality among various other important properties furthermore we show that the concavity property of the auxiliary function enables a geometric interpretation of the random coding exponent and the sphere packing exponent of a classical quantum channel the key component in our proof is an important result from the theory of matrix geometric means

jensen and minkowski inequalities for operator means and anti norms abstract jensen inequalities for positive linear maps of choi and hansen pedersen type are established for a large class of operator matrix means such as some p means and some kubo ando means these results are also extensions of the minkowski determinantal inequality to this end we develop the study of anti norms a notion parallel to the symmetric norms in matrix analysis including functionals like schatten q norms for a parameter q 1 and the minkowski functional det 1 n a

operator algebraic superridigity for sl n ℤ n 3 for n 3 let sln we prove the following superridigity result for in the context of operator algebras let l be the von neumann algebra generated by the left regular representation of let m be a finite factor and let u m be its unitary group let u m be a group homomorphism such that m then either

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

strong converse exponent for classical quantum channel coding we determine the exact strong converse exponent of classical quantum channel coding for every rate above the holevo capacity our form of the exponent is an exact analogue of arimoto s given as a transform of the renyi capacities with parameters alpha 1 it is important to note that unlike in the classical case there are many inequivalent ways to define the renyi divergence of states and hence the renyi capacities of channels our exponent is in terms of the renyi capacities corresponding to a version of the renyi divergences that has been introduced recently in muller lennert et al j math phys 54 12 122203 2013 arxiv 1306 3142 and wilde et al commun math phys 331 2 593 622 2014 arxiv 1306 1586 our result adds to the growing body of evidence that this new version is the natural definition for the purposes of strong converse problems

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

existence and global attractivity of positive periodic solutions for a predator prey model with modified leslie gower holling type ii schemes abstract in this paper by utilizing the coincidence degree theorem and constructing a suitable lyapunov function the predator prey model with modified leslie gower holling type ii schemes is studied some sufficient conditions are obtained for the existence and global attractivity of positive periodic solutions of this model furthermore one example shows that the obtained criteria are easily verifiable

some operator and trace function convexity theorems we consider trace functions a b tr a q 2 b pa q 2 s where a and b are positive n n matrices and ask when these functions are convex or concave we also consider operator convexity concavity of a q 2 b pa q 2 and convexity concavity of the closely related trace functional tr a q 2 b pa q 2 c r the concavity questions are completely resolved thereby settling cases left open by hiai the convexity questions are settled in many cases as a consequence the audenaert datta renyi entropy conjectures are proved for some cases

on non semisplit extensions tensor products and exactness of group c algebras we show the existence of a block diagonal extensionb of the suspensions a of the reduced groupc algebraa c sl 2 such that there is only onec norm on the algebraic tensor productb op b butb is not nuclear even not exact thus the class of exactc algebras is not closed under extensions the existence comes from a new established tensorial duality between the weak expectation property wep of lance and the local variant llp of the lifting property we characterize the local lifting property of separable unitalc algebrasa as follows a has the local lifting property if and only if ext s a is a group wheres a is the suspension ofa if moreovera is the quotient algebra of ac algebra withwep for brevity a isqwep but does not satisfyllp then there exists a quasidiagonal extensionb of the suspensions a by the compact operators such that on the algebraic tensor productb op b there is only onec norm the question if everyc algebra isqwep remains open but we obtain the following results onqwep ac algebrac isqwep if and only ifc isqwep a von neumannii 1 factorn with separable predualn isqwep if and only ifn is a von neumann subfactor of the ultrapower of the hyperfiniteii 1 factor ifg is a maximally almost periodic discrete non amenable group with haagerup s herz schur multiplier constant g 1 then the universal groupc algebrac g is not exact but the reduced groupc albegrac g is exact and isqwep but does not satisfywep andllp we study functiorial properties of the classes ofc algebras satisfyingwep llp resp beingqwep as applications we obtain some unexpected relations between some open questions onc algebras

inequalities for quantum divergences and the audenaert datta conjecture given two density matrices rho and sigma there are a number of different expressions that reduce to the alpha renyi relative entropy of rho with respect to sigma in the classical case i e when rho and sigma commute only those expressions for which the data processing inequality dpi is valid are of potential interest as quantum divergences in quantum information theory audenaert and datta have made a conjecture on the validity of the dpi for an interesting family of quantum generalizations of the alpha renyi relative entropies the alpha z renyi relative entropies they and others have contributed to the partial solution of this conjecture we review the problem its context and the methods that have been used to obtain the results that are known at present presenting a unified treatment of developments that have unfolded in a number of different papers

crossed products of operator systems abstract in this paper we introduce the crossed product construction for a discrete group action on an operator system in analogy to the work of e katsoulis and c ramsey we describe three canonical crossed products arising from such a dynamical system we describe how these crossed product constructions behave under g equivariant maps tensor products and the canonical c covers we show that hyperrigidity is preserved under two of the three crossed products finally using a kavruk s notion of an operator system that detects c nuclearity we give a negative answer to a question on operator algebra crossed products posed by katsoulis and ramsey

permanence and periodicity of a delayed ratio dependent predator prey model with stage structure a periodic ratio dependent predator prey model with time delays and stage structure for both prey and predator is investigated it is assumed that immature individuals and mature individuals of each species are divided by a fixed age and that immature predators do not have the ability to attack prey sufficient conditions are derived for the permanence and existence of positive periodic solutions of the model numerical simulations are presented to illustrate the feasibility of our main results

covering dimension for nuclear c algebras ii the completely positive rank is an analogue of the topological covering dimension defined for nuclear c algebras via completely positive approximations these may be thought of as simplicial approximations of the algebra which leads to the concept of piecewise homogeneous maps and a notion of noncommutative simplicial complexes we introduce a technical variation of completely positive rank and show that the two theories coincide in many important cases furthermore we analyze some of their properties in particular we show that both theories behave nicely with respect to ideals and that they coincide with the covering dimension of the spectrum for certain continuous trace c algebras

estimating quantum chromatic numbers abstract we develop further the new versions of quantum chromatic numbers of graphs introduced by the first and fourth authors we prove that the problem of computation of the commuting quantum chromatic number of a graph is solvable by an sdp algorithm and describe an hierarchy of variants of the commuting quantum chromatic number which converge to it we introduce the tracial rank of a graph a parameter that gives a lower bound for the commuting quantum chromatic number and parallels the projective rank and prove that it is multiplicative we describe the tracial rank the projective rank and the fractional chromatic numbers in a unified manner that clarifies their connection with the commuting quantum chromatic number the quantum chromatic number and the classical chromatic number respectively finally we present a new sdp algorithm that yields a parameter larger than the lovasz number and is yet a lower bound for the tracial rank of the graph we determine the precise value of the tracial rank of an odd cycle

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

coding theorems for compound problems via quantum renyi divergences recently a new notion of quantum renyi divergences has been introduced by muller lennert dupuis szehr fehr and tomamichel and wilde winter and yang which found a number of applications in strong converse theorems here we show that these new renyi divergences are also useful tools to obtain coding theorems in the direct domain of various problems we demonstrate this by giving new and considerably simplified proofs for the achievability parts of stein s lemma with composite null hypothesis universal state compression and the classical capacity of compound classical quantum channels based on single shot error bounds already available in the literature and simple properties of the quantum renyi divergences the novelty of our proofs is that the composite compound coding theorems can be almost directly obtained from the single shot error bounds essentially with the same effort as for the case of simple null hypothesis single source single channel

tsirelson s problem and asymptotically commuting unitary matrices in this paper we consider quantum correlations of bipartite systems having a slight interaction and reinterpret tsirelson s problem and hence kirchberg s and connes s conjectures in terms of finite dimensional asymptotically commuting positive operator valued measures we also consider the systems of asymptotically commuting unitary matrices and formulate the stronger kirchberg conjecture

two approaches to obtain the strong converse exponent of quantum hypothesis testing for general sequences of quantum states we present two general approaches to obtain the strong converse exponent of simple quantum hypothesis testing for correlated quantum states one approach requires that the states satisfy a certain factorization property typical examples of such states are the temperature states of translation invariant finite range interactions on a spin chain the other approach requires the differentiability of a regularized renyi alpha divergence in the parameter alpha typical examples of such states include temperature states of non interacting fermionic lattice systems and classical irreducible markov chains in all cases we get that the strong converse exponent is equal to the hoeffding anti divergence which in turn is obtained from the regularized renyi divergences of the two states

relative weak injectivity of operator system pairs abstract the concept of a relatively weakly injective pair of operator systems is introduced and studied in this paper motivated by relative weak injectivity in the c algebra category e kirchberg 11 proved that the c algebra c f of the free group f on countably many generators characterises relative weak injectivity for pairs of c algebras by means of the maximal tensor product one of the main results of this paper shows that c f also characterises relative weak injectivity in the operator system category a key tool is the theory of operator system tensor products 9 10

the effros marechal topology in the space of von neumann algebras ii we continue our study 9 of the effros marechal topology on the space vn h of all von neumann algebras acting on a fixed separable hilbert space h in particular we prove that factors of each of the types ii1 ii and for fixed 0 1 iii form a dense subset of vn h moreover the density of type i factors or equivalently of injective factors in vn h is proved to be equivalent to famous conjectures by a connes and e kirchberg

a non nuclear c algebra with the weak expectation property and the local lifting property we construct the first example of a c algebra a with the properties in the title this gives a new example of non nuclear a for which there is a unique c norm on a otimes a op this example is of particular interest in connection with the connes kirchberg problem which is equivalent to the question whether c mathbb f 2 which is known to have the llp also has the wep our c algebra a has the same collection of finite dimensional operator subspaces as c mathbb f 2 or c mathbb f infty in addition our example can be made to be quasidiagonal and of similarity degree or length 3 in the second part of the paper we reformulate our construction in the more general framework of a c algebra that can be described as the limit both inductive and projective for a sequence of c algebras c n when each c n is a subquotient of c n 1 we use this to show that for certain local properties of injective non surjective homomorphisms there are c algebras for which the identity map has the same properties as the homomorphisms

on the local lifting property for operator spaces we study the local lifting property for operator spaces this is a natural non commutative analogue of the banach space local lifting property but is very different from the local lifting property studied in c algebra theory we show that an operator space has the local lifting property if and only if it is an l 1 space these operator space are completely isomorphic to the operator subspaces of the operator preduals of von neumann algebras and thus locally reflexive moreover we show that an operator space v has the local lifting property if and only if its operator space dual v is injective

hyperlinearity essentially free actions and l2 invariants the sofic property we prove that connes embedding conjecture holds for the von neumann algebras of sofic groups that is sofic groups are hyperlinear hence we provide some new examples of hyperlinearity we also show that the determinant conjecture holds for sofic groups as well we introduce the notion of essentially free actions and amenable actions and study their properties

generalizing lieb s concavity theorem via operator interpolation abstract we introduce the notion of k trace and use interpolation of operators to prove the joint concavity of the function a b tr k b q 2 k a p k b q 2 s 1 k which generalizes lieb s concavity theorem and its following results from trace to a class of homogeneous functions tr k 1 k here tr k a denotes the k th elementary symmetric polynomial of the eigenvalues of a this result gives an alternative proof for the concavity of a tr k exp h log a 1 k that was obtained and used in a recent work to derive expectation estimates and tail bounds on partial spectral sums of random matrices

a submajorization of carlen and lieb convexity abstract we show the following function on m tuples of positive operators in finite von neumann algebra m p a 1 a 2 a m k 1 m a k p 1 p l e m is jointly convex for 1 p 2 and for any symmetric norm l e m associated with m

herrero s approximation problem for quasidiagonal operators let t be a quasidiagonal operator on a separable hilbert space it is shown that there exists a sequence of operators tn such that dim c tn and t tn 0 if and only if c t is exact

from wigner yanase dyson conjecture to carlen frank lieb conjecture abstract in this paper we study the joint convexity concavity of the trace functions p q s a b tr b q 2 k a p k b q 2 s p q s r where a and b are positive definite matrices and k is any fixed invertible matrix we will give full range of p q s r 3 for p q s to be jointly convex concave for all k as a consequence we confirm a conjecture of carlen frank and lieb in particular we confirm a weaker conjecture of audenaert and datta and obtain the full range of z for z renyi relative entropies to be monotone under completely positive trace preserving maps we also give simpler proofs of many known results including the concavity of p 0 1 p for 0 p 1 which was first proved by epstein using complex analysis the key is to reduce the problem to the joint convexity concavity of the trace functions p 1 p 1 a b tr k a p k b 1 p 1 p 1 using a variational method

local properties of ternary rings of operators and their linking c algebras abstract we show that some local properties such as nuclearity exactness and local reflexivity of ternary rings of operators tros are closely related to the local properties of their linking c algebras we also show some equivalent conditions for nuclear tros and show that haagerup s decomposition property for completely bounded maps and pisier s norm can be naturally generalized to tros

connes embedding conjecture and sums of hermitian squares we show that connes embedding conjecture on von neumann algebras is equivalent to the existence of certain algebraic certificates for a polynomial in noncommuting variables to satisfy the following nonnegativity condition the trace is nonnegative whenever self adjoint contraction matrices of the same size are substituted for the variables these algebraic certificates involve sums of hermitian squares and commutators we prove that they always exist for a similar nonnegativity condition where elements of separable ii1 factors are considered instead of matrices under the presence of connes conjecture we derive degree bounds for the certificates

almost periodic dynamics of a delayed three level food chain model abstractthis paper is concerned with the dynamics of a three level food chain model with time delays by means of mawhin s continuation theorem of coincidence degree theory we investigate the existence of positive almost periodic solutions in a three level food chain model with time delays a set of sufficient conditions for the existence of at least one positive almost periodic solution of the model is obtained in addition the global asymptotical stability of the almost periodic solution of the above model is also studied finally two examples and simulations are also given to illustrate the main results in this paper

positive periodic solutions of neutral lotka volterra system with feedback control with the help of a continuation theorem based on gaines and mawhin s coincidence degree easily verifiable criteria are established for the global existence of positive periodic solutions of neutral lotka volterra system with periodic delays and feedback control our results extend and improve existing results and have further applications in population dynamics

amenability and exactness for dynamical systems and their c algebras we study the relations between amenability resp amenability at infinity of c dynamical systems and equality or nuclearity resp exactness of the corresponding crossed products

concavity of certain matrix trace and norm functions ii abstract we refine epstein s method to prove joint concavity convexity of matrix trace functions of lieb type tr f a p 1 2 b q a p 1 2 and symmetric anti norm functions of the form f a p b q where and are positive linear maps is an operator mean and f x with a certain power is an operator monotone function on 0 moreover the variational method of carlen frank and lieb is extended to general non decreasing convex concave functions on 0 so that we prove joint concavity convexity of more trace functions of lieb type

almost periodic solution of the non autonomous two species competitive model with stage structure abstract sufficient conditions are obtained for the existence of a unique globally attractive strictly positive componentwise almost periodic solution of a non autonomous almost periodic competitive two species model with a stage structure in one species an example together with its numeric simulations shows the feasibility of our main results our result generalizes the main results of zeng et al g z zeng l s chen l h sun y liu permanence and the existence of the periodic solution of the non autonomous two species competitive model with stage structure adv complex syst 7 3 4 2004 385 393

on matrix inequalities between the power means counterexamples abstract we prove that the known sufficient conditions on the real parameters p q for which the matrix power mean inequality a p b p 2 1 p a q b q 2 1 q holds for every pair of matrices a b 0 are indeed best possible the proof proceeds by constructing 2 2 counterexamples the best possible conditions on p q for which a p 1 p a q 1 q holds for every unital positive linear map and a 0 are also clarified

c algebras associated with groups with kazhdan s property t has exhibited block diagonal operators on separable hilbert spaces which are not norm limits of generators of singly generated finite dimensional c algebras it turns out that voiculescu s construction which is based upon a certain class of groups with property t can be put into a more general context involving c algebras which arise very naturally from such groups it is these c algebras which are the subject of this paper as well as giving a natural setting in which to view voiculescu s result these c algebras have almost fortuitously a number of other important properties which are very easily established like the full c algebras of free groups these c algebras are not

an approximate universal coefficient theorem an approximate universal coefficient theorem auct for certain c algebras is established we present a proof that kirchberg phillips s classification theorem for separable nuclear purely infinite simple c algebras is valid for c algebras satisfying the auct instead of the uct it is proved that two versions of auct are in fact the same we also show that c algebras that are locally approximated by c algebras satisfying the auct satisfy the auct as an application we prove that certain simple c algebras which are locally type i are in fact isomorphic to simple ah algebras as another application we show that a sequence of residually finite dimensional c algebras which are asymptotically nuclear and which asymptotically satisfies the auct can be embedded into the same simple af algebra

synchronous correlation matrices and connes embedding conjecture in the work of paulsen et al j funct anal in press preprint arxiv 1407 6918 the concept of synchronous quantum correlation matrices was introduced and these were shown to correspond to traces on certain c algebras in particular synchronous correlation matrices arose in their study of various versions of quantum chromatic numbers of graphs and other quantum versions of graph theoretic parameters in this paper we develop these ideas further focusing on the relations between synchronous correlation matrices and microstates we prove that connes embedding conjecture is equivalent to the equality of two families of synchronous quantum correlation matrices we prove that if connes embedding conjecture has a positive answer then the tracial rank and projective rank are equal for every graph we then apply these results to more general non local games

c algebras generated by operator systems an operator systemx such thatx is ac algebra and such that the canonical embedding ofxinx is a unital complete isometry is called ac system ifais a unitalc algebra andlis a closed left ideal ofa thena l l has a natural operator system structure relative to which it is ac system it is shown that any separablec system is of this form for some separablea and that an arbitrary inseparablec system is an inductive limit of separablec systems associated with any operator systemxis a universalc algebrac u x which containsxas a generating subsystem and is maximal among suchc algebras in the sense that any other suchc algebra is canonically a homomorphic image ofc u x ifxis additionally ac system then thec subalgebrac r x ofx generated byxis minimal amongc algebras containingxas a generating subsystem in the sense thatc r x is canonically a homomorphic image of any other suchc algebra it follows that there is a canonical homomorphism c u x c r x which extends the identity map onx whenxis ac algebra of dimension greater than 1 is never injective one of the main results of the paper is that there exists a separable nuclearc systemxcontainingm2 c for which is an isomorphism this implies that for any embedding ofxas an operator subsystem of ac algebraa thec subalgebra ofagenerated byxis isomorphic toc u x moreoverc u m2 c is notc exact andc u m2 c c u x from which it follows thatc u x and hencea are not exactc algebras thusx though a nuclear operator system cannot be embedded in a nuclearc algebra

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

polyhedral duality in bell scenarios with two binary observables for the bell scenario with two parties and two binary observables per party it is known that the no signaling polytope is the polyhedral dual polar of the bell polytope computational evidence suggests that this duality also holds for three parties using ideas of werner wolf ukowski and brukner we prove this for any number of parties by describing a simple linear bijection mapping facet bell inequalities to extremal no signaling boxes and vice versa furthermore a symmetry based technique for extending bell inequalities respectively no signaling boxes with two binary observables from n parties to n 1 parties is described the mermin klyshko family of bell inequalities arises in this way as well as 11 of the 46 classes of facet bell inequalities for three parties finally we ask whether the set of quantum correlations is self dual with respect to our transformation we find this not to be the case in general although it holds for two parties on the level of correlations this self duality implies tsirelson s bound for the chsh inequality

maurey s factorization theory for operator spaces we prove an operator space version of maurey s theorem which claims that every absolutely p 1 summing map on c k is automatically absolutely q summing for q p our results imply in particular that every completely bounded map from b h with values in pisier s operator space oh is completely p summing for p 2 this fails for p 2 as applications we obtain eigenvalue estimates for translation invariant maps defined on the von neumann algebra vn g associated with a discrete group g we also develop a notion of cotype which is compatible with factorization results on noncommutative lp spaces

permanence and periodicity of a delayed ratio dependent predator prey model with holling type functional response and stage structure a periodic and delayed ratio dependent predator prey system with holling type iii functional response and stage structure for both prey and predator is investigated it is assumed that immature predator and mature individuals of each species are divided by a fixed age and immature predator do not have the ability to attack prey sufficient conditions are derived for the permanence and existence of positive periodic solution of the model numerical simulations are presented to illustrate the feasibility of our main results

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