Approximation properties and absence of Cartan subalgebra for free Araki-Woods factors
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2010
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| _version_ | 1866911059526287360 |
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| author | Houdayer, Cyril Ricard, Eric |
| author_facet | Houdayer, Cyril Ricard, Eric |
| contents | We show that all the free Araki-Woods factors $Γ(H_\R, U_t)"$ have the complete metric approximation property. Using Ozawa-Popa's techniques, we then prove that every nonamenable subfactor $\mathcal{N} \subset Γ(H_\R, U_t)"$ which is the range of a normal conditional expectation has no Cartan subalgebra. We finally deduce that the type ${\rm III_1}$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1006_3689 |
| institution | arXiv |
| publishDate | 2010 |
| record_format | arxiv |
| spellingShingle | Approximation properties and absence of Cartan subalgebra for free Araki-Woods factors Houdayer, Cyril Ricard, Eric Operator Algebras Functional Analysis 46L07, 46L10, 46L54 We show that all the free Araki-Woods factors $Γ(H_\R, U_t)"$ have the complete metric approximation property. Using Ozawa-Popa's techniques, we then prove that every nonamenable subfactor $\mathcal{N} \subset Γ(H_\R, U_t)"$ which is the range of a normal conditional expectation has no Cartan subalgebra. We finally deduce that the type ${\rm III_1}$ 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. |
| title | Approximation properties and absence of Cartan subalgebra for free Araki-Woods factors |
| topic | Operator Algebras Functional Analysis 46L07, 46L10, 46L54 |
| url | https://arxiv.org/abs/1006.3689 |