标题： 论$L^p$算子交叉积的Takai对偶性，II 显示英文标题

标题： On the Takai duality of $L^p$ operator crossed products, II

摘要： 本文旨在研究由N. C. Phillips提出的$L^p$Takai对偶性问题。 设$G$为一个可数离散阿贝尔群，$A$为一个可分的单位$L^p$算子代数且具有$p\in [1,\infty)$，$\alpha$为$G$在$A$上的一个等距作用。 当 $A$ 是 $p$-不可压缩的且具有唯一的 $L^p$ 算子矩阵范数时，本文证明了迭代的 $L^p$ 算子交叉乘积 $F^{p}(\hat{G},F^p(G,A,\alpha),\hat{\alpha})$ 与 $\overline{M}_{G}^{p}\otimes_{p}A$ 同构当且仅当 $p=2$。 显示英文摘要

摘要： This paper aims to study the $L^p$ Takai duality problem raised by N. C. Phillips. Let $G$ be a countable discrete Abelian group, $A$ be a separable unital $L^p$ operator algebra with $p\in [1,\infty)$, and $\alpha$ be an isometric action of $G$ on $A$. When $A$ is $p$-incompressible and has unique $L^p$ operator matrix norms, it is proved in this paper that the iterated $L^p$ operator crossed product $F^{p}(\hat{G},F^p(G,A,\alpha),\hat{\alpha})$ is isometrically isomorphic to $\overline{M}_{G}^{p}\otimes_{p}A$ if and only if $p=2$.