Topological centers of the n-th dual of module actions

Document Type : Research Paper


1 University of Mohghegh Ardabili

2 Amirkabir University of Technology


We study the topological centers of $nth$ dual of Banach $mathcal{A}$-modules and we extend some propositions from Lau and "{U}lger into $n-th$ dual of Banach $mathcal{A}-modules$ where $ngeq 0$ is even number. Let   $mathcal{B}$   be a Banach  $mathcal{A}-bimodule$. By using some new conditions, we show that
 $ Z^ell_{mathcal{A}^{(n)}}(mathcal{B}^{(n)})=mathcal{B}^{(n)}$ and
 $ Z^ell_{mathcal{B}^{(n)}}(mathcal{A}^{(n)})=mathcal{A}^{(n)}$. We get some conclusions on  group algebras.