On multiplicity and free absorption for free Araki-Woods factors

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 $\Gamma (\mu ,n)$ associated to a measure and a multiplicity function $n$ may non-trivially depend on the multiplicity function.

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• Structural results for free Araki-Woods factors and their continuous cores
• Free Araki-Woods factors and Connes' bicentralizer problem
• Classification of a family of non almost periodic free Araki-Woods factors
• A new construction of factors of type $\mathrm{II}{\mathrm{I}}_1$
• Free quasi-free states and factors of type III (after D. Shlyakhtenko)