GENERALIZED REVERSE CAUCHY INEQUALITY AND APPLICATIONS TO OPERATOR MEANS

被引：1

作者：

Osaka, Hiroyuki ^{[1
]}

Tsurumi, Yukihiro ^{[1
]}

Wada, Shuhei ^{[2
]}

机构：

[1] Ritsumeikan Univ, Dept Math Sci, Kusatsu, Shiga 5258577, Japan

[2] Kisarazu Coll, Natl Inst Technol, Dept Informat & Comp Engn, Kisarazu Chiba 2920041, Japan

来源：

JOURNAL OF MATHEMATICAL INEQUALITIES | 2018年 / 12卷 / 04期

关键词：

Operator means; operator monotone functions; reverse Cauchy inequality;

D O I：

10.7153/jmi-2018-12-79

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let sigma be an operator mean in the sense of Kubo-Ando and let del(alpha) a be a weighted arithmetric mean. If Tr(A sigma B) >= Tr(A del B-alpha - max{alpha, 1 - alpha}vertical bar A - B vertical bar) holds for all positive semidefinite matrices A,B, then there exists beta is an element of [0,1] such that sigma = del(beta) .

引用

页码：1029 / 1039

页数：11

共 23 条

[21] Maps between positive cones of operator algebras preserving a measure of the difference between arithmetic and geometric means
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[23] Inequalities for generalized derivations of operator monotone functions in norm ideals of compact operators (vol 586, pg 43, 2020)
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LINEAR ALGEBRA AND ITS APPLICATIONS, 2020, 599 : 201 - 204

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