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

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 \"{ U}lger into $n-th$ dual of Banach $A-modules$ where $n\geq 0$ 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.

Categories: math.FA