Some characterizations of the trace norm triangle equality
type: Item
instance of: scholarly article
title: Some characterizations of the trace norm triangle equality
zbMATH Open document ID: 1339.47024
author: Yu-E Li
author: Yuan Li
published in: Linear Algebra and its Applications
publication date: 2015-08-24T00:00:00Z
review text: The authors obtain a characterization of the equality \(\|A+B\|_{1}=\|A\|_{1}+\|B\|_{1}\) to hold for trace-class operators \(A\) and \(B\), where \(\|X\|_{1}\) means the trace norm. In particular, the authors show that, for trace-class operators \(A\) and \(B\), \(\|A+B\|_{1}=\|A\|_{1}+\|B\|_{1}\) if and only if \(|A+B|=|A|+|B|\). This is related to a result (Theorem 2.3) in [\textit{T. Ando} and \textit{T. Hayashi}, J. Oper. Theory 58, No. 1, 463--468 (2007; Zbl 1150.47001)]. In the present article, the authors use a rather different technique to prove this characterization. Moreover, a characterization of the equality \(\|A+A^{*}\|_{1}=\|A\|_{1}+\|A^{*}\|_{1}\) is obtained.
reviewed by: Takeaki Yamazaki
Mathematics Subject Classification ID: 47B10
Mathematics Subject Classification ID: 47B15
Mathematics Subject Classification ID: 47A63
zbMATH DE Number: 6475069
zbMATH Keywords: trace-class operator
zbMATH Keywords: trace norm
zbMATH Keywords: triangle inequality
MaRDI profile type: Publication
full work available at URL: j.laa.2015.07.011
OpenAlex ID: W1027172759
cites work: Q5444344
cites work: A characterization of minimal Hermitian matrices
cites work: Norm inequalities for partitioned operators and an application
cites work: Best approximation by diagonal compact operators
cites work: Q4702980
cites work: \(c_ p\)
cites work: An inequality for trace ideals
cites work: Inequalities for the Schatten p-norm. III
cites work: Inequalities for the Schatten p-Norm. IV
cites work: Q3263053
cites work: Q5063168
cites work: Q3857325
cites work: Linear orthogonality preservers of standard operator algebras
cites work: The case of equality in the matrix-valued triangle inequality
cites work: Isometries of non-commutative Lp-spaces
DOI: 10.1016/J.LAA.2015.07.011
description: scientific article; zbMATH DE number 6475069