Free Araki-Woods factors and Connes' bicentralizer problem
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2008
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| _version_ | 1866918094083981312 |
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| author | Houdayer, Cyril |
| author_facet | Houdayer, Cyril |
| contents | We show that for any free Araki-Woods factor $\mathcal{M} = Γ(H_\R, U_t)"$ of type ${\rm III_1}$, the bicentralizer of the free quasi-free state $φ_U$ is trivial. Using Haagerup's Theorem, it follows that there always exists a faithful normal state $ψ$ on $\mathcal{M}$ such that $(\mathcal{M}^ψ)' \cap \mathcal{M} = \C$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_0809_3827 |
| institution | arXiv |
| publishDate | 2008 |
| record_format | arxiv |
| spellingShingle | Free Araki-Woods factors and Connes' bicentralizer problem Houdayer, Cyril Operator Algebras 46L10, 46L54 We show that for any free Araki-Woods factor $\mathcal{M} = Γ(H_\R, U_t)"$ of type ${\rm III_1}$, the bicentralizer of the free quasi-free state $φ_U$ is trivial. Using Haagerup's Theorem, it follows that there always exists a faithful normal state $ψ$ on $\mathcal{M}$ such that $(\mathcal{M}^ψ)' \cap \mathcal{M} = \C$. |
| title | Free Araki-Woods factors and Connes' bicentralizer problem |
| topic | Operator Algebras 46L10, 46L54 |
| url | https://arxiv.org/abs/0809.3827 |