Let F be an algebraically closed field of characteristic zero. We give a complete classification of finite dimensional simple superalgebras over F endowed with a graded automorphism or a ...pseudoautomorphism.
Two bounded linear operators A and B are parallel with respect to a norm ‖⋅‖ if ‖A+μB‖=‖A‖+‖B‖ for some scalar μ with |μ|=1. Characterization is obtained for bijective linear maps sending parallel ...bounded linear operators to parallel bounded linear operators with respect to the Ky-Fan k-norms.
Let A and B be two unital prime complex *-algebras such that A has a
nontrivial projection. In this paper, we study the structure of the
bijective mappings ? ? A ? B preserving sum of products ?1ab* ...+ ?2b*a +
?3ba* (resp., ?1ab* + ?2b*a + ?3a*b), where the scalars {?k}3k =1 are
rational numbers satisfying some conditions.
Arveson's extension theorem guarantees that every completely positive map defined on an operator system can be extended to a completely positive map defined on the whole C*-algebra containing it. An ...analogous statement where complete positivity is replaced by positivity is known to be false. A natural question is whether extendibility could still hold for positive maps satisfying stronger conditions, such as being unital and norm 1. Here we provide three counterexamples showing that positive norm-one unital maps defined on an operator subsystem of a matrix algebra cannot be extended to a positive map on the full matrix algebra. The first counterexample is an unextendible positive unital map with unit norm, the second counterexample is an unextendible positive unital isometry on a real operator space, and the third counterexample is an unextendible positive unital isometry on a complex operator space.
The category
of Banach spaces and linear maps of norm
is locally
-presentable but not locally finitely presentable. We prove, however, that
is locally finitely presentable in the enriched sense over ...complete metric spaces. Moreover, in this sense, pure morphisms are just ideals of Banach spaces. We characterize classes of Banach spaces approximately injective with respect to sets of morphisms having finite-dimensional domains and separable codomains.
The behaviour of quasi-linear maps on C(K)-spaces Cabello Sánchez, Félix; Castillo, Jesús M.F.; Salguero-Alarcón, Alberto
Journal of mathematical analysis and applications,
07/2019, Letnik:
475, Številka:
2
Journal Article
Recenzirano
In this paper we combine topological and functional analysis methods to prove that a non-locally trivial quasi-linear map defined on a C(K) must be nontrivial on a subspace isomorphic to c0. We ...conclude the paper with a few examples showing that the result is optimal, and providing an application to the existence of nontrivial twisted sums of ℓ1 and c0.
A new method of using the numerical range of a matrix to bound the optimal value of certain optimization problems over real tensor product vectors is presented. This bound is stronger than the ...trivial bounds based on eigenvalues and can be computed significantly faster than bounds provided by semidefinite programming relaxations. Numerous applications to other hard linear algebra problems are discussed, such as showing that a real subspace of matrices contains no rank-one matrix, and showing that a linear map acting on matrices is positive.
Linear reduced dynamics I Sargolzahi
Iranian Journal of Physics Research,
08/2020, Letnik:
20, Številka:
2
Journal Article
Odprti dostop
Consider an open quantum, system interacting with its environment. Whether the reduced dynamics of the system can be given by a linear map or not is an important question in the theory of open ...quantum systems. Dominy, Shabani and Lidar have proposed a general framework for linear Hermitian reduced dynamics. In addition, it has been shown that their framework is, in fact, the most general one: The reduced dynamics of the system is linear if and only if it can be formulated within the Dominy-Shabani-Lidar framework. This result has been given in a rather abstract way. Here, we want to give another proof for it, in a more illustrative manner.
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