Linear maps preserving numerical radius of tensor products of matrices
نویسندگان
چکیده
منابع مشابه
Linear Maps Preserving Numerical Radius of Tensor Products of Matrices
Let m,n ≥ 2 be positive integers. Denote by Mm the set of m×m complex matrices and by w(X) the numerical radius of a square matrix X. Motivated by the study of operations on bipartite systems of quantum states, we show that a linear map φ : Mmn →Mmn satisfies w(φ(A⊗B)) = w(A⊗B) for all A ∈Mm and B ∈Mn if and only if there is a unitary matrix U ∈Mmn and a complex unit ξ such that φ(A⊗B) = ξU(φ1(...
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For a positive integer n, let Mn be the set of n×n complex matrices. Suppose m,n ≥ 2 are positive integers and k ∈ {1, . . . ,mn− 1}. Denote by Wk(X) the k-numerical range of a matrix X ∈Mmn. It is shown that a linear map φ : Mmn →Mmn satisfies Wk(φ(A⊗B)) = Wk(A⊗B) for all A ∈Mm and B ∈Mn if and only if there is a unitary U ∈Mmn such that one of the following holds. (i) For all A ∈Mm, B ∈Mn, φ(...
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Let F (A) be the numerical range or the numerical radius of a square matrix A. Denote by A◦B the Schur product of two matrices A and B. Characterizations are given for mappings on square matrices satisfying F (A ◦ B) = F (φ(A) ◦ φ(B)) for all matrices A and B. Analogous results are obtained for mappings on Hermitian matrices. 2000 Mathematics Subject Classification. 15A04, 15A18, 15A60
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For a positive integer n, let Mn be the set of n × n complex matrices. Suppose ‖ · ‖ is the Ky Fan k-norm with 1 ≤ k ≤ mn or the Schatten p-norm with 1 ≤ p ≤ ∞ (p 6= 2) on Mmn, where m,n ≥ 2 are positive integers. It is shown that a linear map φ : Mmn →Mmn satisfying ‖A⊗B‖ = ‖φ(A⊗B)‖ for all A ∈Mm and B ∈Mn if and only if there are unitary U, V ∈ Mmn such that φ has the form A ⊗ B 7→ U(φ1(A) ⊗ ...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2013
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2013.05.030