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

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 Mn(C), which seems to be new insofar a...

Full description

Saved in:
Bibliographic Details
Published in:Bulletin des sciences mathématiques 2015-06, Vol.139 (4), p.400-419
Main Authors: Bercovici, H., Collins, B., Dykema, K., Li, W.S.
Format: Article
Language:English
Subjects:
Finite von Neumann algebra
Littlewood–Richardson coefficients
Singular numbers
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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 Mn(C), which seems to be new insofar as we do not require A and B to be invertible.
ISSN:0007-4497
1952-4773
DOI:10.1016/j.bulsci.2014.10.002