On multiplicity and free absorption for free Araki-Woods factors

2003/02/18 by Dimitri Shlyakhtenko, Shlyakhtenko, Dimitri · 2 citations
Mathematics · #46L54 #Advanced Operator Algebra Research #FOS: Mathematics #Operator Algebras (math.OA) #Random Matrices and Applications #Spectral Theory in Mathematical Physics #math.OA #msc:46L54

paper · pdf · doi:10.48550/arxiv.math/0302217

arxiv created 2003/02/18 · openalex publication_date 2003/02/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that Ozawa's recent results on solid von Neumann algebras imply that there are free Araki-Woods factors, which fail to have free absorption. We also show that a free Araki-Woods factors Γ(μ, n) associated to a measure and a multiplicity function n may non-trivially depend on the multiplicity function.

Cited by

• A new construction of factors of type \rm III₁
• Free Araki-Woods factors and Connes' bicentralizer problem

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