The Topological Centers Of Module Actions

TL;DR

This paper explores the topological centers of module actions in Banach spaces, extending existing propositions, introducing new properties, and examining their relationships with applications in dual groups.

Contribution

It generalizes propositions on topological centers for Banach module actions, introduces $Lw^*w$- and $Rw^*w$-properties, and investigates their connections with dual group applications.

Findings

Extended propositions to general Banach module actions

Introduced $Lw^*w$- and $Rw^*w$-properties for Banach bimodules

Established relationships between topological centers and new properties

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.