论文标题
局部紧凑的群体对交叉产物的正式和内部可正常作用和近似特性
Amenable and inner amenable actions and approximation properties for crossed products by locally compact groups
论文作者
论文摘要
通过利用跨乘积的自然模块结构，在代理组的傅立叶代数上利用了跨代数的局部紧凑型组对von Neumann代数的可正常作用。跨产品的注射率的表征是分散组上Anantharaman-Delaroche的结果。本地紧凑型组在$ C^*$ - 代数方面的可正常作用以相同的方式进行了研究，并且该动作的敏感性与相应的交叉产品的核性有关。进行了一项调查，以表明$ c^*$ - 代数的这种可及行动的概念满足了许多预期属性。引入了局部紧凑型组动作的内部舒适性概念，并以平均参数的形式给出了许多应用，将跨产品von Neumann代数的近似属性与基本$ W**$动力学系统组件的属性的属性相关联。我们使用这些结果来回答最近的公共汽车 - Echterhoff-Willett问题。
Amenable actions of locally compact groups on von Neumann algebras are investigated by exploiting the natural module structure of the crossed product over the Fourier algebra of the acting group. The resulting characterisation of injectivity for crossed products generalises a result of Anantharaman-Delaroche on discrete groups. Amenable actions of locally compact groups on $C^*$-algebras are investigated in the same way, and amenability of the action is related to nuclearity of the corresponding crossed product. A survey is given to show that this notion of amenable action for $C^*$-algebras satisfies a number of expected properties. A notion of inner amenability for actions of locally compact groups is introduced, and a number of applications are given in the form of averaging arguments, relating approximation properties of crossed product von Neumann algebras to properties of the components of the underlying $w^*$-dynamical system. We use these results to answer a recent question of Buss-Echterhoff-Willett.
