TY - JOUR ID - 35723 TI - Topological Centers and Factorization of Certain Module Actions JO - Sahand Communications in Mathematical Analysis JA - SCMA LA - en SN - 2322-5807 AU - Barootkoob, Sedigheh AD - Department of Mathematics, Faculty of Basic Sciences, University of Bojnord, P.O. Box 1339, Bojnord, Iran. Y1 - 2019 PY - 2019 VL - 15 IS - 1 SP - 203 EP - 215 KW - Topological centers KW - Module actions KW - Arens regular KW - Strongly Arens irregular DO - 10.22130/scma.2018.76242.344 N2 - 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. UR - https://scma.maragheh.ac.ir/article_35723.html L1 - https://scma.maragheh.ac.ir/article_35723_a8368ffd978c33879a6cf9ae4f4947df.pdf ER -