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For Banach left and right module actions, we extend some propositions fromLau and $\ddot{U}lger$ into general situations and we establish therelationships between topological centers of module actions. We also introducethe new concepts as $Lw^*w$-property and $Rw^*w$-property for Banach$A-bimodule$ $B$ and we obtain some conclusions in the topological center ofmodule actions and Arens regularity of Banach algebras. we also study somefactorization properties of left module actions and we find some relations ofthem and topological centers of module actions. For Banach algebra $A$, weextend the definition of $\ast-involution$ algebra into Banach $A-bimodule$ $B$with some results in the factorizations of $B^*$. We have some applications ingroup algebras.

The topological centers and factorization properties of module actions and $\ast-involution$ algebras