Generalized s-numbers of τ-measurable operators

Thierry Fack and Hideki Kosaki

Vol. 123 (1986), No. 2, 269–300

DOI: 10.2140/pjm.1986.123.269

Abstract

We give a self-contained exposition on generalized s-numbers of τ-measurable operators affiliated with a semi-finite von Neumann algebra. As applications, dominated convergence theorems for a gage and convexity (or concavity) inequalities are investigated. In particular, relation between the classical L^p-norm inequalities and inequalities involving generalized s-numbers due to A. Grothendieck, J. von Neumann, H. Weyl and the first named author is clarified. Also, the Haagerup L^p- spaces (associated with a general von Neumann algebra) are considered.

Mathematical Subject Classification 2000

Primary: 46L10

Secondary: 47A30, 46L50

Milestones

Received: 28 February 1985

Revised: 22 July 1985

Published: 1 June 1986