Arens regularity and weak topological center of module actions

Details Arens regularity and weak topological center of module actions Arens regularity and weak topological center of module actions

2010-06-30

arxiv.org/abs/1006.5810v1

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 we will find some relations between this concept and the topological center of $A^{**}$. We also extend this new definition into the 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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