Ando-Hiai inequality and Furuta inequality

被引：17

作者：

Fujii, Masatoshi ^{[1
]}

Kamei, Eizaburo

机构：

[1] Osaka Kyoiku Univ, Dept Math, Osaka 5828582, Japan

[2] Maebashi Inst Technol, Maebashi, Gumma 3710816, Japan

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2006年 / 416卷 / 2-3期

关键词：

positive operators; operator mean; Lowner-Heinz inequality; Furuta inequality; grand Furuta inequality; chaotic order;

D O I：

10.1016/j.laa.2005.12.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let A, B > 0, the positive operators on a Hilbert space. Ando-Hiai inequality (AH) and Furuta inequality (F) are given as follows: A, B > 0; A#B-alpha <= 1 double right arrow A(r)#B-alpha(r)<= I for r >= 1, and A >= B > 0 double right arrow A-r#(p+r)/(1+r) Bp <= B <= A. We show these inequalities imply each other. (c) 2005 Elsevier Inc. All rights reserved.

引用

页码：541 / 545

页数：5

共 14 条

[1]

[Anonymous], LINEAR ALGEBRA APPL

[2]

FUJII M, 1990, J OPERAT THEOR, V23, P67

[3] FURUTA INEQUALITY AND ITS APPLICATION TO ANDO THEOREM [J].