Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 28, No. 2, pp. 189-196 (2012)

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

O. T. Mewomo and G. Akinbo

University of Agriculture (Abeokuta) and Obafemi Awolowo University

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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