On the approximate and weak approximate amenability of the second dual of Banach algebras

Abstract: Let $A$ be a Banach algebra. We investigate the relations between the bounded approximate amenability of $A"$ and Arens regularity of $A$ and the role of topological centres in the approximate amenability of $A"$. We also find conditions under which approximate weak amenability of $A"$ necessitates that of $A$. In particular, we show that if $S$ is an infinite weakly cancellative semigroup, then the approximate weak amenability of $l^{1}(S)"$ necessitates that of $l^{1}(S)$.

Keywords: Banach algebra, derivation, second dual, approximately amenable, approximately weakly amenable

Classification (MSC2000): 46H20; 46H10, 46H25

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