Selfless W$^*$-probability spaces and Connes' bicentralizer problem
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909005791625216 |
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| author | Houdayer, Cyril Marrakchi, Amine |
| author_facet | Houdayer, Cyril Marrakchi, Amine |
| contents | We introduce the notion of selfless W$^*$-probability space and study its connection with Connes' bicentralizer problem. In particular, we show that if $M$ is a separable type ${\rm III_1}$ factor with trivial bicentralizer, then $(M, φ)$ is selfless for every faithful normal state $φ\in M_\ast$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_11409 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Selfless W$^*$-probability spaces and Connes' bicentralizer problem Houdayer, Cyril Marrakchi, Amine Operator Algebras 46L10, 46L36, 46L54 We introduce the notion of selfless W$^*$-probability space and study its connection with Connes' bicentralizer problem. In particular, we show that if $M$ is a separable type ${\rm III_1}$ factor with trivial bicentralizer, then $(M, φ)$ is selfless for every faithful normal state $φ\in M_\ast$. |
| title | Selfless W$^*$-probability spaces and Connes' bicentralizer problem |
| topic | Operator Algebras 46L10, 46L36, 46L54 |
| url | https://arxiv.org/abs/2511.11409 |