A note on ideal C$^\ast$-completions and amenability
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929272043601920 |
|---|---|
| author | Kochanek, Tomasz |
| author_facet | Kochanek, Tomasz |
| contents | For a discrete group $G$, we consider certain ideals $\mathcal{I}\subset c_0(G)$ of sequences with prescribed rate of convergence to zero. We show that the equality between the full group C$^\ast$-algebra of $G$ and the C$^\ast$-completion $\mathrm{C}_{\mathcal{I}}^\ast(G)$ in the sense of Brown and Guentner implies that $G$ is amenable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_06945 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note on ideal C$^\ast$-completions and amenability Kochanek, Tomasz Functional Analysis For a discrete group $G$, we consider certain ideals $\mathcal{I}\subset c_0(G)$ of sequences with prescribed rate of convergence to zero. We show that the equality between the full group C$^\ast$-algebra of $G$ and the C$^\ast$-completion $\mathrm{C}_{\mathcal{I}}^\ast(G)$ in the sense of Brown and Guentner implies that $G$ is amenable. |
| title | A note on ideal C$^\ast$-completions and amenability |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2403.06945 |