标题： 群作用在紧空间上的可约性及相关的巴拿赫代数 显示英文标题

标题： Amenability of group actions on compact spaces and the associated Banach algebras

摘要： 对于拓扑群$G$，可分性可以通过卷积巴拿赫代数$L^1(G)$的可分性来表征。 这里一个巴拿赫代数$A$被称为可分的，如果从$A$到任何对偶类型$A$-$A$-巴拿赫双模的每个有界导子都是内导子。 我们将这一经典结果扩展到紧豪斯多夫空间上的离散群作用的情况。 通过引入与该作用自然相关的巴拿赫代数，并采用适合削弱的巴拿赫代数可分性概念，我们得到了可分作用的类似表征。 作为引理，我们也证明了可分作用的一个不动点性质，该性质加强了 Dong 和 Wang（2015）的定理。 显示英文摘要

摘要： 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).