Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/23995
Title: Linear maps preserving Ky Fan norms and Schatten norms of tensor products of matrices
Authors: Fosner, A
Huang, Z
Li, CK
Sze, NS 
Keywords: Complex matrix
Ky Fan k-norm
Linear preserver
Schatten p-norm
Spectral norm
Tensor product
Issue Date: 2013
Publisher: Society for Industrial and Applied Mathematics
Source: SIAM journal on matrix analysis and applications, 2013, v. 34, no. 2, p. 673-685 How to cite?
Journal: SIAM journal on matrix analysis and applications 
Abstract: 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 ≠ 2) on M mn, 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 → U(φ1(A) ⊗ φ2(B))V , where φs(X) is either the identity map X → X or the transposition map X → Xt. The results are extended to tensor space Mn1 ⊗ ⋯ ⊗ Mnm of higher level. The connection of the problem to quantum information science is mentioned.
URI: http://hdl.handle.net/10397/23995
ISSN: 0895-4798
EISSN: 1095-7162
DOI: 10.1137/120891794
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