Generalized Log-Majorization and Multivariate Trace Inequalities

被引：9

作者：

Hiai, Fumio ^{[1
]}

Konig, Robert ^{[2
]}

Tomamichel, Marco ^{[3
,4
]}

机构：

[1] Tohoku Univ, Sendai, Miyagi, Japan

[2] Tech Univ Munich, Inst Adv Study & Zentrum Math, Garching, Germany

[3] Univ Sydney, Sch Phys, Sydney, NSW, Australia

[4] Univ Technol Sydney, Ctr Quantum Software & Informat, Sydney, NSW, Australia

来源：

ANNALES HENRI POINCARE | 2017年 / 18卷 / 07期

关键词：

D O I：

10.1007/s00023-017-0569-y

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We show that recent multivariate generalizations of the Araki-Lieb-Thirring inequality and the Golden-Thompson inequality (Sutter et al. in Commun Math Phys, 2016. doi: 10.1007/s00220-016-2778-5) for Schatten norms hold more generally for all unitarily invariant norms and certain variations thereof. The main technical contribution is a generalization of the concept of log-majorization which allows us to treat majorization with regard to logarithmic integral averages of vectors of singular values.

引用

页码：2499 / 2521

页数：23

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