Some inequalities for spectral geometric mean with applications

被引：1

作者：

Furuichi, Shigeru ^{[1
,2
]}

Seo, Yuki ^{[3
]}

机构：

[1] Nihon Univ, Coll Humanities & Sci, Dept Informat Sci, Setagaya Ku, Tokyo 1568850, Japan

[2] SIMATS, Saveetha Sch Engn, Dept Math, Chennai 602105, Tamil Nadu, India

[3] Osaka Kyoiku Univ, Dept Math Educ, Osaka, Japan

来源：

LINEAR & MULTILINEAR ALGEBRA | 2025年 / 73卷 / 07期

关键词：

Spectral geometric mean; operator geometric mean; Kantorovich constant; operator norm; <roman>log</roman>-majorization; R & eacute; nyi mean; relative entropy; RELATIVE ENTROPY; LOG-MAJORIZATION;

D O I：

10.1080/03081087.2024.2433512

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Recently, the spectral geometric mean has been studied by some papers. In this paper, we first estimate the H & ouml;lder-type inequality of the spectral geometric mean of positive invertible operators on the Hilbert space for all real order in terms of the generalized Kantorovich constant and show the relation between the weighted geometric mean and the spectral geometric one under the usual operator order. Moreover, we show their operator norm version. Next, in the matrix case, we show the log-majorization for the spectral geometric mean and their applications. Among others, we show the order relation among three quantum Tsallis relative entropies. Finally we give a new lower bound of the Tsallis relative entropy.

引用

页码：1508 / 1527

页数：20

共 42 条

[31]

Matsumoto K., ARXIV

[32] Operator spectral geometric versus geometric mean [J].