论文标题
在$ c^*$ - 代数和跌倒捆绑上的典型群体的动作
Amenability for actions of étale groupoids on $C^*$-algebras and Fell bundles
论文作者
论文摘要
我们将雷诺对第二个可数的行动的概念概括，hausdorff，étalegropsoids在可分离的$ c^*$ - 代数上，并表明，每当$ c^*$ - 代数以核心作用的$ c^*$ - 核心的核能是核的。在第二个可数的Fell Bundles的更一般环境中，Hausdorff，étalegroupoids，我们介绍了Exel近似属性的版本。我们证明，每当单位束为核时，近似特性意味着横截面代数的核性。对于与群体固体作用相关的跌落束，我们表明近似属性意味着基础作用的衡量性舒适性。
We generalize Renault's notion of measurewise amenability to actions of second countable, Hausdorff, étale groupoids on separable $C^*$-algebras and show that measurewise amenability characterizes nuclearity of the crossed product whenever the $C^*$-algebra acted on is nuclear. In the more general context of Fell bundles over second countable, Hausdorff, étale groupoids, we introduce a version of Exel's approximation property. We prove that the approximation property implies nuclearity of the cross-sectional algebra whenever the unit bundle is nuclear. For Fell bundles associated to groupoid actions, we show that the approximation property implies measurewise amenability of the underlying action.
