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Amenability and topological centres of the second duals of Banach algebras. (English) Zbl 1029.46116

Summary: Let \({\mathfrak A}\) be a Banach algebra and let \({\mathfrak A}^{**}\) be the second dual algebra of \({\mathfrak A}\) endowed with the first or the second Arens product. We investigate relations between amenability of \({\mathfrak A}^{**}\) and Arens regularity of \({\mathfrak A}\) and the role of topological centres in amenability of \({\mathfrak A}^{**}\). We also find conditions under which weak amenability of \({\mathfrak A}^{**}\) implies weak amenability of \({\mathfrak A}\).

MSC:

46M18 Homological methods in functional analysis (exact sequences, right inverses, lifting, etc.)
46H05 General theory of topological algebras
46H20 Structure, classification of topological algebras
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