The Topological Centers Of Module Actions

TL;DR

This paper investigates the topological centers of the n-th duals of Banach A-modules, extending existing propositions and establishing new conditions under which these centers coincide with the modules themselves.

Contribution

It extends previous results on topological centers to n-th duals of Banach modules and introduces new conditions for their equality with the modules.

Findings

Established conditions for topological centers to equal the modules.

Extended propositions from Lau and Ulger to n-th duals.

Provided conclusions applicable to dual groups.

Abstract

In this paper, we will study the topological centers of $n-th$ dual of Banach $A-module$ and we extend some propositions from Lau and $\ddot{U}lger$ into $n-th$ dual of Banach $A-modules$. Let $B$ be a Banach $A-bimodule$. By using some new conditions, we show that ${{Z}^\ell}_{A^{(n)}}(B^{(n)})=B^{(n)}$ and ${{Z}^\ell}_{B^{(n)}}(A^{(n)})=A^{(n)}$. We also have some conclusions in dual groups.