Document Type : Research Paper
Author
Department of Mathematics, Faculty of Basic Sciences, University of Bojnord, P.O. Box 1339, Bojnord, Iran.
Abstract
Let $A$ be a Banach algebra and $X$ be a Banach $A$-bimodule with the left and right module actions $\pi_\ell: A\times X\rightarrow X$ and $\pi_r: X\times A\rightarrow X$, respectively. In this paper, we study the topological centers of the left module action $\pi_{\ell_n}: A\times X^{(n)}\rightarrow X^{(n)}$ and the right module action $\pi_{r_n}:X^{(n)}\times A\rightarrow X^{(n)}$, which inherit from the module actions $\pi_\ell$ and $\pi_r$, 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.
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Main Subjects
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