In this paper, we establish some relationships between Left and right weakly completely continuous operators and topological centers of module actions and relationships between the factorization and the kinds of amenability. We de ne the locally topological center of the left and right module actions and investigate some of its properties. Also, we want to examine some conditions that under those the duality of a Banach algebra is strongly Connes-amenable. Finally, we generalize the concept of the weakly strongly connes amenable to even dual in higher orders.
