Amenability of group actions on compact spaces and the associated Banach algebras
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913916280373248 |
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| author | Awazu, Hikaru |
| author_facet | Awazu, Hikaru |
| contents | For a topological group $G$, amenability can be characterized by the amenability of the convolution Banach algebra $L^1(G)$. Here a Banach algebra $A$ is called amenable if every bounded derivation from $A$ into any dual--type $A$--$A$--Banach bimodule is inner. We extend this classical result to the case of discrete group actions on compact Hausdorff spaces. By introducing a Banach algebra naturally associated with the action and adopting a suitably weakened notion of amenability for Banach algebras, we obtain an analogous characterization of amenable actions. As a lemma, we also proved a fixed--point property for amenable actions that strengthens the theorem of Dong and Wang (2015). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_08357 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Amenability of group actions on compact spaces and the associated Banach algebras Awazu, Hikaru Functional Analysis Group Theory Operator Algebras For a topological group $G$, amenability can be characterized by the amenability of the convolution Banach algebra $L^1(G)$. Here a Banach algebra $A$ is called amenable if every bounded derivation from $A$ into any dual--type $A$--$A$--Banach bimodule is inner. We extend this classical result to the case of discrete group actions on compact Hausdorff spaces. By introducing a Banach algebra naturally associated with the action and adopting a suitably weakened notion of amenability for Banach algebras, we obtain an analogous characterization of amenable actions. As a lemma, we also proved a fixed--point property for amenable actions that strengthens the theorem of Dong and Wang (2015). |
| title | Amenability of group actions on compact spaces and the associated Banach algebras |
| topic | Functional Analysis Group Theory Operator Algebras |
| url | https://arxiv.org/abs/2504.08357 |