Noncommutative Lp structure encodes exactly Jordan structure

2003/09/22 by David K. Sherman, David Sherman, Sherman, David · 2 citations
Mathematics · #46B04 #46L52 #47B49 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Holomorphic and Operator Theory #Operator Algebras (math.OA) #math.OA #msc:46B04 #msc:46L52 #msc:47B49

paper · pdf · doi:10.48550/arxiv.math/0309365

14 pages, to appear in J. Funct. Anal. A step in the earlier proof was invalid for finite type I algebras

openalex publication_date 2003/09/22 · arxiv created 2004/09/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that for all 1 ≤ p ≤ ∞, p not 2, the Lp spaces associated to two von Neumann algebras M,N are isometrically isomorphic if and only if M and N are Jordan *-isomorphic. This follows from a noncommutative Lp Banach-Stone theorem: a specific decomposition for surjective isometries of noncommutative Lp spaces.

Cited by

• Noncommutative Orlicz spaces over W*-algebras
• W*-algebras and noncommutative integration

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