Salvato in:
| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2407.11738 |
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Sommario:
- 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 $M'\cap (M\rtimes_α G)=\mathbb{C}$.