Linear maps preserving the higher numerical ranges of tensor products of matrices
نویسندگان
چکیده
منابع مشابه
Linear Maps Preserving the Higher Numerical Ranges of Tensor Products of Matrices
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 Mn be the semigroup of n× n complex matrices under the usual multiplication, and let S be different subgroups or semigroups in Mn including the (special) unitary group, (special) general linear group, the semigroups of matrices with bounded ranks. Suppose Λk(A) is the rank-k numerical range and rk(A) is the rank-k numerical radius of A ∈ Mn. Multiplicative maps φ : S → Mn satisfying rk(φ(A)...
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ژورنال
عنوان ژورنال: Linear and Multilinear Algebra
سال: 2013
ISSN: 0308-1087,1563-5139
DOI: 10.1080/03081087.2013.790386