Topological centers and factorization of certain module actions. (English) Zbl 1438.46057
Summary: 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.
MSC:
| 46H25 | Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX) |
| 46H20 | Structure, classification of topological algebras |
References:
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