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Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 28, No. 2, pp. 189-196 (2012)
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On the approximate and weak approximate amenability of the second dual of Banach algebras

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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

**Full text of the article:**

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