共查询到20条相似文献,搜索用时 12 毫秒
1.
Kyung Hoon Han 《Journal of Functional Analysis》2011,261(4):999-386
We prove that an operator system S is nuclear in the category of operator systems if and only if there exist nets of unital completely positive maps φλ:S→Mnλ and ψλ:Mnλ→S such that ψλ°φλ converges to idS in the point-norm topology. Our proof is independent of the Choi-Effros-Kirchberg characterization of nuclear C?-algebras and yields this characterization as a corollary. We give an explicit example of a nuclear operator system that is not completely order isomorphic to a unital C?-algebra. 相似文献
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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 -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 -nuclearity, we give a negative answer to a question on operator algebra crossed products posed by Katsoulis and Ramsey. 相似文献
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Nathan S. Feldman 《Proceedings of the American Mathematical Society》1999,127(9):2685-2695
We shall use a -algebra approach to study operators of the form where is subnormal and is normal. We shall determine the spectral properties for these operators, and find the minimal normal extension and the dual operator. We also give a necessary condition for to contain a compact operator and a sufficient condition for the algebraic equivalence of and .
We also consider the existence of a homomorphism satisfying . We shall characterize the operators such that exists for every operator .
The problem of when is unitarily equivalent to is considered. Complete results are given when and are positive operators with finite multiplicity functions and has compact self-commutator. Some examples are also given.
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Jaspal Singh Aujla 《Linear algebra and its applications》2000,310(1-3):43-47
Jensen's operator inequality characterizes operator convex functions of two variables (F. Hansen, Proc. Amer. Math. Soc. 125 (1997) 2093–2102). We give a simplified proof of this theorem formulated for matrices. 相似文献
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Bojan Magajna 《Transactions of the American Mathematical Society》1996,348(6):2427-2440
Tensor products of Calgebras over an abelian Walgebra are studied. The minimal Cnorm on is shown to be just the quotient of the minimal Cnorm on if or is exact.
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Nathaniel Johnston David W. Kribs Vern I. Paulsen 《Journal of Functional Analysis》2011,260(8):2407-2423
We examine k-minimal and k-maximal operator spaces and operator systems, and investigate their relationships with the separability problem in quantum information theory. We show that the matrix norms that define the k-minimal operator spaces are equal to a family of norms that have been studied independently as a tool for detecting k-positive linear maps and bound entanglement. Similarly, we investigate the k-super minimal and k-super maximal operator systems that were recently introduced and show that their cones of positive elements are exactly the cones of k-block positive operators and (unnormalized) states with Schmidt number no greater than k, respectively. We characterize a class of norms on the k-super minimal operator systems and show that the completely bounded versions of these norms provide a criterion for testing the Schmidt number of a quantum state that generalizes the recently-developed separability criterion based on trace-contractive maps. 相似文献
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本文在L—fuzzy模范畴中,建立了相应的张量积,给出了它的结构性、存在性与唯一性定理,并讨论了张量函子与Hom函子的伴随性。所得结果为通常张量积的“良好推广”(goodextension)。 相似文献
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Friedrich W. Bauer 《Mathematische Annalen》1973,205(4):303-315
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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 and . 相似文献
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Andreas Weber 《Journal of Mathematical Analysis and Applications》2009,351(2):603-1139
We study tensor products of strongly continuous semigroups on Banach spaces that satisfy the hypercyclicity criterion, the recurrent hypercyclicity criterion or are chaotic. 相似文献
13.
DONG Zhe 《数学年刊B辑(英文版)》2003,24(3):323-330
This paper studies the tensor product RN RM of Jacobson radicals in nest algebras, and obtains that RN RM = {T∈B(H1 H2) : T(N M)(?)N_ M_, N∈N,M∈M}; and based on the characterization of rank-one operators in RN RM,it is proved that if N, M are non-trivial then RN RM=R if and only if N, M are continuous. 相似文献
14.
Matthew Ondrus 《代数通讯》2013,41(8):2506-2523
We describe the action of the center of the quantum group Uq () on the tensor product V ? L(λ) of an infinite-dimensional representation V having an infinitesimal character χτ and an irreducible finite-dimensional Uq () representation L(λ) of highest weight λ. We apply this result in order to describe the tensor product of a Whittaker module and a finite-dimensional simple module for the algebra Uq(l2). 相似文献
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The quantum doubles of a certain class of rank two pointed Hopf algebras are considered. The socle of the tensor product of two such modules is computed, and formulas similar to the ones in [4] are obtained. Cases when such a tensor product is completely irreducible are also given in the last section. 相似文献
18.
The aim of this article is to start a metric theory of homogeneous polynomials in the category of operator spaces. For this purpose we take advantage of the basic fact that the space Pm(E) of all m-homogeneous polynomials on a vector space E can be identified with the algebraic dual of the m -th symmetric tensor product ⊗m,sE. Given an operator space V, we study several different types of completely bounded polynomials on V which form the operator space duals of ⊗m,sV endowed with related operator structures. Of special interest are what we call Haagerup, Kronecker, and Schur polynomials – polynomials associated with different types of matrix products. 相似文献
19.
Kyung Hoon Han 《Journal of Mathematical Analysis and Applications》2010,367(2):516-386
We establish a relationship between Schreiner's matrix regular operator space and Werner's (nonunital) operator system. For a matrix ordered operator space V with complete norm, we show that V is completely isomorphic and complete order isomorphic to a matrix regular operator space if and only if both V and its dual space V∗ are (nonunital) operator systems. 相似文献
20.
Tensor methods for large sparse systems of nonlinear equations 总被引:1,自引:0,他引:1
This paper introduces tensor methods for solving large sparse systems of nonlinear equations. Tensor methods for nonlinear equations were developed in the context of solving small to medium-sized dense problems. They base each iteration on a quadratic model of the nonlinear equations, where the second-order term is selected so that the model requires no more derivative or function information per iteration than standard linear model-based methods, and hardly more storage or arithmetic operations per iteration. Computational experiments on small to medium-sized problems have shown tensor methods to be considerably more efficient than standard Newton-based methods, with a particularly large advantage on singular problems. This paper considers the extension of this approach to solve large sparse problems. The key issue considered is how to make efficient use of sparsity in forming and solving the tensor model problem at each iteration. Accomplishing this turns out to require an entirely new way of solving the tensor model that successfully exploits the sparsity of the Jacobian, whether the Jacobian is nonsingular or singular. We develop such an approach and, based upon it, an efficient tensor method for solving large sparse systems of nonlinear equations. Test results indicate that this tensor method is significantly more efficient and robust than an efficient sparse Newton-based method, in terms of iterations, function evaluations, and execution time. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.Work supported by the Mathematical, Information, and Computational Sciences Division subprogram of the Office of Computational and Technology Research, US Department of Energy, under Contract W-31-109-Eng-38, by the National Aerospace Agency under Purchase Order L25935D, and by the National Science Foundation, through the Center for Research on Parallel Computation, under Cooperative Agreement No. CCR-9120008.Research supported by AFOSR Grants No. AFOSR-90-0109 and F49620-94-1-0101, ARO Grants No. DAAL03-91-G-0151 and DAAH04-94-G-0228, and NSF Grant No. CCR-9101795. 相似文献