Characterization of singular numbers of products of operators in matrix algebras and finite von Neumann algebras

被引：3

作者：

Bercovici, H. ^{[1
]}

Collins, B. ^{[2
,3
,4
]}

Dykema, K. ^{[5
]}

Li, W. S. ^{[6
]}

机构：

[1] Indiana Univ, Dept Math, Bloomington, IN 47405 USA

[2] Kyoto Univ, Dept Math, Kyoto 6068501, Japan

[3] Univ Ottawa, Dept Math & Stat, Ottawa, ON K1N 6N5, Canada

[4] Univ Lyon 1, CNRS, Inst Camille Jordan, F-69622 Villeurbanne, France

[5] Texas A&M Univ, Dept Math, College Stn, TX 77843 USA

[6] Georgia Inst Technol, Sch Math, Atlanta, GA 30332 USA

来源：

BULLETIN DES SCIENCES MATHEMATIQUES | 2015年 / 139卷 / 04期

基金：

美国国家科学基金会; 加拿大自然科学与工程研究理事会;

关键词：

Singular numbers; Finite von Neumann algebra; Littlewood-Richardson coefficients; EIGENVALUE INEQUALITIES; CONJECTURE; SUMS;

D O I：

10.1016/j.bulsci.2014.10.002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We characterize in terms of inequalities the possible generalized singular numbers of a product AB of operators A and B having given generalized singular numbers, in an arbitrary finite von Neumann algebra. We also solve the analogous problem in matrix algebras M-n (C), which seems to be new insofar as we do not require A and B to be invertible. (C) 2014 Elsevier Masson SAS. All rights reserved.

引用

页码：400 / 419

页数：20

共 16 条

[1] Local systems on P1-S for S a finite set [J].