Arens Regularity And The Topological Centers Of Module Actions

TL;DR

This paper explores the properties of topological centers in Banach module actions, extending existing propositions, introducing new properties, and applying findings to dual groups.

Contribution

It generalizes previous results on topological centers, introduces $Lw^*w$- and $Rw^*w$-properties, and investigates their relations within Banach bimodules.

Findings

Extended propositions from Lau and Ulger to general Banach modules.

Established relationships between topological centers and new properties.

Applied results to dual groups.

Abstract

In this article, for Banach left and right module actions, we will extend some propositions from Lau and $\ddot{U}lger$ into general situations and we establish the relationships between topological centers of module actions. We also introduce the new concepts as $Lw^*w$-property and $Rw^*w$-property for Banach $A-bimodule$ $B$ and we investigate the relations between them and topological center of module actions. We have some applications in dual groups.