A Hilbert-Schmidt norm Inequality for positive semidefinite matrices related to a question of Bourin

被引：2

作者：

Hayajneh, Mostafa ^{[1
]}

Hayajneh, Saja ^{[2
]}

Kittaneh, Fuad ^{[2
]}

机构：

[1] Yarmouk Univ, Dept Math, Irbid, Jordan

[2] Univ Jordan, Dept Math, Amman, Jordan

来源：

POSITIVITY | 2022年 / 26卷 / 03期

关键词：

Trace; Hilbert-Schmidt norm; Positive semidefinite matrix; Bourin's question; Inequality; ANDO; HIAI;

D O I：

10.1007/s11117-022-00924-y

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let A and B be positive semidefinite matrices of the same size. Using a trace inequality of Ando, Hiai, and Okubo, we prove that parallel to B1-t A(2t-1) B1-t + A(1-t )B(2t-1) A(1-t) parallel to(2) <= parallel to A + B parallel to(2) for t is an element of [1/2, 3/4], where parallel to.parallel to(2) denotes the Hilbert-Schmidt norm. This gives an affimative answer to a question posed by Hayajneh and Kittaneh regarding an open question of Bourin in the case of the Hilbert-Schmidt norm.

引用

页数：9

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