  In this article, for Banach left and right module actions, we will extend
some propositions from Lau and $\ddot{U}lger$ into general situations and we
establish the relationships between topological centers of module actions. We
also introduce the new concepts as $Lw^*w$-property and $Rw^*w$-property for
Banach $A-bimodule$ $B$ and we investigate the relations between them and
topological center of module actions. We have some applications in dual groups.
