Linear Operators Preserving the Numerical Radius of Matrices
نویسندگان
چکیده
منابع مشابه
Linear Operators Preserving the Numerical Range (Radius) on Triangular Matrices
We characterize those linear operators on triangular or diagonal matrices preserving the numerical range or radius.
متن کاملLinear Operators Preserving the Numerical Range ( Radius ) on Triangular
We characterize those linear operators on triangular or diagonal matrices preserving the numerical range or radius.
متن کاملLinear 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(...
متن کاملMaps preserving the joint numerical radius distance of operators
Denote the joint numerical radius of an m-tuple of bounded operators A = (A1, . . . , Am) by w(A). We give a complete description of maps f satisfying w(A − B) = w(f(A) − f(B)) for any two m-tuples of operators A = (A1, . . . , Am) and B = (B1, . . . , Bm). We also characterize linear isometries for the joint numerical radius, and maps preserving the joint numerical range of A. AMS Classificati...
متن کاملSchur product of matrices and numerical radius (range) preserving maps
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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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1987
ISSN: 0002-9939
DOI: 10.2307/2046460