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正规性及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大多数经典Banach谐波分析的代数，以解决给定Banach代数A为经常出现Arens，并且A在理想情况下是理想的。在本文的第二部分中，我们研究了一类具有乘数有界近似恒等式的Banach代数的双峰的拓扑中心。