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.
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页码：400 / 419
页数：20
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