Title: Twisted crossed products of Banach algebras Show Chinese title

Title: 巴拿赫代数的扭曲交叉乘积

Abstract: Given a locally compact group $G$, a nondegenerate Banach algebra $A$ with a contractive approximate identity, a twisted action $(\alpha, \sigma)$ of $G$ on $A$, and a family $\mathcal{R}$ of uniformly bounded representations of $A$ on Banach spaces, we define the twisted crossed product $F_\mathcal{R}(G,A,\alpha, \sigma)$. When $\mathcal{R}$ consists of contractive representations, we show that $F_\mathcal{R}(G,A,\alpha, \sigma)$ is a Banach algebra with a contractive approximate identity, which can also be characterized by an isometric universal property. As an application, we specialize to the $L^p$-operator algebra setting, defining both the $L^p$-twisted crossed product and the reduced version. Finally, we give a generalization of the so-called Packer-Raeburn trick to the $L^p$-setting, showing that any $L^p$-twisted crossed product is "stably" isometrically isomorphic to an untwisted one. Show Chinese abstract

Abstract: 给定一个局部紧群$G$，一个具有压缩逼近单位的非退化巴拿赫代数$A$，一个由$G$在$A$上的扭曲作用$(\alpha, \sigma)$，以及一个由$A$在巴拿赫空间上的统一有界表示族$\mathcal{R}$，我们定义扭曲的交叉积$F_\mathcal{R}(G,A,\alpha, \sigma)$。 当$\mathcal{R}$包含压缩表示时，我们证明$F_\mathcal{R}(G,A,\alpha, \sigma)$是一个具有压缩近似单位的巴拿赫代数，也可以通过一个等距的普遍性质来表征。 作为应用，我们专门考虑$L^p$算子代数的设定，定义了$L^p$-扭曲交叉积以及其约化版本。 最后，我们将所谓的 Packer-Raeburn 技巧推广到$L^p$的设定中，表明任何$L^p$-扭曲交叉积都“稳定地”等距同构于一个无扭曲的交叉积。