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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.11738 |
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| _version_ | 1866912281818824704 |
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| author | Morando, Basile |
| author_facet | Morando, Basile |
| contents | We show that, given a continuous action $α$ of a locally compact group $G$ on a factor $M$, the relative commutant $M'\cap(M\rtimes_α G)$ is contained in $M\rtimes_α H$ where $H$ is the subgroup of elements acting without spectral gap. As a corollary, we answer a question of Marrakchi and Vaes by showing that if $M$ is semifinite and $α_g$ is not approximately inner for all $g\neq 1$, then $M'\cap (M\rtimes_α G)=\mathbb{C}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_11738 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Strictly outer actions of locally compact groups: beyond the full factor case Morando, Basile Operator Algebras We show that, given a continuous action $α$ of a locally compact group $G$ on a factor $M$, the relative commutant $M'\cap(M\rtimes_α G)$ is contained in $M\rtimes_α H$ where $H$ is the subgroup of elements acting without spectral gap. As a corollary, we answer a question of Marrakchi and Vaes by showing that if $M$ is semifinite and $α_g$ is not approximately inner for all $g\neq 1$, then $M'\cap (M\rtimes_α G)=\mathbb{C}$. |
| title | Strictly outer actions of locally compact groups: beyond the full factor case |
| topic | Operator Algebras |
| url | https://arxiv.org/abs/2407.11738 |