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

Mewomo, O. T. and Akinbo, G. (2012) On the approximate and weak approximate amenability of the second dual of Banach algebras. ACTA MATHEMATICA ACADEMIAE PAEDAGOGICAE NYÍREGYHÁZIENSIS, 28 (2). pp. 189-196. ISSN 0866-0174

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Abstract

Let A be a Banach algebra. We investigate the relations between the bounded approximate amenability of A00 and Arens regularity of A and the role of topological centres in the approximate amenability of A00 . We also find conditions under which approximate weak amenability of A00 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) 00 necessitates that of l 1 (S).

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