Factorization properties and topological centers of left module actions

TL;DR

This paper explores the mathematical properties of Banach left module actions, focusing on topological centers and their relation to multipliers and factorization, with applications to dual groups.

Contribution

It extends existing propositions to more general settings and clarifies the relationship between topological centers and module action properties.

Findings

Established connections between topological centers and multiplier properties.

Extended propositions to broader Banach module contexts.

Provided applications to dual group structures.

Abstract

For a Banach left module action, we will extend some propositions from Lau and $\ddot{U}$lger and others into general situations and we establish the relationships between topological centers of the left module action with the multiplier and factorization properties of left module actions. We have some applications in the dual groups.