Based on Katznelson–Tzafriri Theorem on power bounded operators, we prove in this paper a theorem, which applies to the most of the classical Banach algebras of harmonic analysis associated with locally compact groups, to deal with the problems when a given Banach algebra A is Arens regular and when A is an ideal in its bidual. In the second part of the paper, we study the topological center of the bidual of a class of Banach algebras with a multiplier bounded approximate identity.

中文翻译：

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一类与局部紧群相关的 Banach 代数的 Arens 正则性和相关问题的统一方法

基于关于幂有界算子的 Katznelson-Tzafriri 定理，我们在本文中证明了一个定理，该定理适用于与局部紧群相关的调和分析的大多数经典 Banach 代数，以处理给定 Banach 代数 A 是Arens 正则且当 A 是其双双的理想时。在论文的第二部分，我们研究了一类具有乘数有界近似恒等式的 Banach 代数的二元拓扑中心。