The Arens Regularity and Weak Topological Center of Module Actions

Details The Arens Regularity and Weak Topological Center of Module Actions The Arens Regularity and Weak Topological Center of Module Actions

2010-10-26

arxiv.org/abs/1010.5414v1

Mathematics

Functional Analysis

Scientific paper

Let $A$ be a Banach algebra and $A^{**}$ be the second dual of it. We define $\tilde{Z}_1(A^{**})$ as a weak topological center of $A^{**}$ with respect to first Arens product and find some relations between it and the topological center of $A^{**}$. We also extend this new definition into module actions and find relationship between weak topological center of module actions and reflexivity or Arens regularity of some Banach algebras, and we investigate some applications of this new definition in the weak amenability of some Banach algebras.

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