Topological Centers and Factorization of Certain Module Actions
Journal: Sahand Communications in Mathematical Analysis (Vol.15, No. 1)Publication Date: 2019-07-01
Authors : Sedigheh Barootkoob;
Page : 203-215
Keywords : Topological centers; Module actions; Arens regular; Strongly Arens irregular;
Abstract
Let $A$ be a Banach algebra and $X$ be a Banach $A$-bimodule with the left and right module actions $pi_ell: Atimes Xrightarrow X$ and $pi_r: Xtimes Arightarrow X$, respectively. In this paper, we study the topological centers of the left module action $pi_{ell_n}: Atimes X^{(n)}rightarrow X^{(n)}$ and the right module action $pi_{r_n}:X^{(n)}times Arightarrow X^{(n)}$, 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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Last modified: 2019-07-27 18:10:17