A NORM INEQUALITY FOR PAIRS OF COMMUTING POSITIVE SEMIDEFINITE MATRICES

被引：20

作者：

Audenaert, Koenraad M. R. ^{[1
,2
]}

机构：

[1] Royal Holloway Univ London, Dept Math, Egham TW20 0EX, Surrey, England

[2] Univ Ghent, Dept Phys & Astron, B-9000 Ghent, Belgium

来源：

ELECTRONIC JOURNAL OF LINEAR ALGEBRA | 2015年 / 30卷

关键词：

Matrix Inequality; Unitarily Invariant Norm; Positive semidefinite matrix;

D O I：

10.13001/1081-3810.2829

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For i = 1, ... , k, let A(i) and B-i be positive semidefinite matrices such that, for each i, A(i) commutes with B-i. It is shown that, for any unitarily invariant norm, vertical bar vertical bar vertical bar Sigma(k)(i-1)A(i)B(i)vertical bar vertical bar vertical bar <= vertical bar vertical bar vertical bar (Sigma(k)(i-1)A(i)(Sigma B-k(i-1)i)vertical bar vertical bar vertical bar. The k = 2 case was recently conjectured by Hayajneh and Kittaneh and proven by them for the trace norm and the Hilbert-Schmidt norm. A simple application of this norm inequality answers a question of Bourin in the affirmative.

引用

页码：80 / 84

页数：5

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