Approximation properties and absence of Cartan subalgebra for free Araki–Woods factors |
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Authors: | Cyril Houdayer Éric Ricard |
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Institution: | aCNRS – ENS Lyon, UMPA UMR 5669, 69364 Lyon cedex 7, France;bLaboratoire de Mathématiques, Université de Franche-Comté, 16 route de Gray, 25030 Besançon, France |
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Abstract: | We show that all the free Araki–Woods factors Γ″(HR,Ut) have the complete metric approximation property. Using Ozawa–Popa?s techniques, we then prove that every nonamenable subfactor N⊂Γ″(HR,Ut) which is the range of a normal conditional expectation has no Cartan subalgebra. We finally deduce that the type III1 factors constructed by Connes in the ?70s can never be isomorphic to any free Araki–Woods factor, which answers a question of Shlyakhtenko and Vaes. |
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Keywords: | MSC: 46L07 46L10 46L54 |
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