Duality between some linear preserver problems. III: c-spectral norms and (skew)-symmetric matrices with fixed singular values
type: Item
instance of: scholarly article
title: Duality between some linear preserver problems. III: c-spectral norms and (skew)-symmetric matrices with fixed singular values
zbMATH Open document ID: 0712.15028
DOI: 10.1016/0024-3795(91)90007-J
author: Chi-Kwong Li
author: Nam-Kiu Tsing
published in: Linear Algebra and its Applications
publication date: 1991-01-01T00:00:00Z
review text: This paper is a continuation of the authors' earlier papers [part I: Linear Multilinear Algebra 23, No.4, 353-362 (1988; Zbl 0668.15014) and part II: Linear Algebra Appl. 110, 181-212 (1988; Zbl 0655.15026)]. Here they consider the problem of a linear preserver on the matrix space V of all \(n\times n\) symmetric and skew-symmetric matrices over the complex field C or the real field R. They prove that the linear operator T: \(V\to V\) satisfies \(\| T(A)=_ d=\| A\|_ c\) for all A in V if and only if \(T^*(\Sigma (d))=\Sigma (c)\). Necessary and sufficient conditions for the existence of such operators and their forms are obtained. In the process of proving this, they obtain a characterization of extreme points of the unit ball of V with respect to \(\| \cdot \|_ c\).
reviewed by: Shaokuan Li
Mathematics Subject Classification ID: 15A60
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 15B57
Mathematics Subject Classification ID: 15A04
zbMATH DE Number: 4171134
zbMATH Keywords: singular values
zbMATH Keywords: isometry
zbMATH Keywords: c-spectral norms
zbMATH Keywords: linear preserver
zbMATH Keywords: matrix space
zbMATH Keywords: skew-symmetric matrices
zbMATH Keywords: extreme points
MaRDI profile type: Publication
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Wikidata QID: Q127720579
description: scientific article; zbMATH DE number 4171134