论文标题
在本地紧凑的组上正常的动态系统
Amenable dynamical systems over locally compact groups
论文作者
论文摘要
我们建立了对任意本地紧凑型组的$ w^*$ - 和$ c^*$ - 动态系统的几个新特征。在$ w^* $ - 设置中，我们表明，舒适性等同于（1）重点属性，（2）存在完全积极的net net，完全具有$（m，g，α）$ clivering点弱*的完全肯定的herz-schur乘数弱*与$ g \ bar {\ ltimes} m $的身份。 In the $C^*$-setting, we prove that amenability of $(A,G,α)$ is equivalent to an analogous Herz-Schur multiplier approximation of the identity of the reduced crossed product $G\ltimes A$, as well as a particular case of the positive weak approximation property of Bédos and Conti (generalized the locally compact setting).当$ z（a^{**}）= z（a）^{**} $时，遵循的是舒适性等于exel和ng的1阳性近似属性。特别是，当$ a = c_0（x）$是可交换的时，$（c_0（x），g，α）$的舒适性与拓扑修正性$ g $ -space $（g，x）$相吻合。我们的结果回答了文献中的2个开放问题； Anantharaman之一 - 德拉罗什（Delaroche），以及最近的公共汽车 - eChterhoff-willett的工作。
We establish several new characterizations of amenable $W^*$- and $C^*$-dynamical systems over arbitrary locally compact groups. In the $W^*$-setting we show that amenability is equivalent to (1) a Reiter property and (2) the existence of a certain net of completely positive Herz-Schur multipliers of $(M,G,α)$ converging point weak* to the identity of $G\bar{\ltimes}M$. In the $C^*$-setting, we prove that amenability of $(A,G,α)$ is equivalent to an analogous Herz-Schur multiplier approximation of the identity of the reduced crossed product $G\ltimes A$, as well as a particular case of the positive weak approximation property of Bédos and Conti (generalized the locally compact setting). When $Z(A^{**})=Z(A)^{**}$, it follows that amenability is equivalent to the 1-positive approximation property of Exel and Ng. In particular, when $A=C_0(X)$ is commutative, amenability of $(C_0(X),G,α)$ coincides with topological amenability the $G$-space $(G,X)$. Our results answer 2 open questions from the literature; one of Anantharaman--Delaroche, and one from recent work of Buss--Echterhoff--Willett.
