Lipschitz continuity of the absolute value and Riesz projections in symmetric operator spaces

P. G. Dodds, T. K. Dodds, B. De Pagter, F. A. Sukochev

Research output: Contribution to journalArticlepeer-review

38 Citations (Scopus)

Abstract

A principal result of the paper is that ifEis a symmetric Banach function space on the positive half-line with the Fatou property then, for all semifinite von Neumann algebras (M, τ), the absolute value mapping is Lipschitz continuous on the associated symmetric operator spaceE(M, τ) with Lipschitz constant depending only onEif and only ifEhas non-trivial Boyd indices. It follows that if M is any von Neumann algebra, then the absolute value map is Lipschitz continuous on the corresponding HaagerupLp-space, provided 1<p<∞.

Original languageEnglish
Pages (from-to)28-69
Number of pages42
JournalJournal of Functional Analysis
Volume148
Issue number1
DOIs
Publication statusPublished - 1 Aug 1997

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