Topological centers of $n-$th dual of module actions

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 Ülger into $n-th$ dual of Banach $A-modules$ where $n\ge 0$ is even number. 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 group algebras.