Topological Centers and Factorization of Certain Module Actions

Let a be a banach algebra and x be a banach a- bimodule with the left and right module actions πℓ:a×x→x and πr:x×a→x, respectively. in this paper, we study the topological centers of the left module action πℓn:a×x^(n)→x^(n) and the right module action πrn:x^(n)×a→x^(n), which inherit from the module actions πℓ and πr, and also the topological centers of their adjoints, from the factorization property point of view, and then, we investigate conditions under which these bilinear maps are arens regular or strongly arens irregular.