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Arens regularity of module actions and weak amenability of Banach algebras. (English) Zbl 1363.46036
The authors give some results concerning criteria of Arens regularity of Banach algebras in the sense of R. Arens [Proc. Am. Math. Soc. 2, 839–848 (1951; Zbl 0044.32601)]. A Banach algebra \(A\) is said to be weakly amenable if every derivation from \(A\) into its dual \(A^\ast\) is inner. Similarly, the notion of \(n\)-weakly amenable Banach algebras is introduced, following the paper of Y. Zhang [Trans. Am. Math. Soc. 354, No. 10, 4131–4151 (2002; Zbl 1008.46019)]. The authors also study \(n\)-weak amenability of module extensions of Banach algebras and weak\(^\ast\)-continuous derivations on Banach algebras.

MSC:
46H25 Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)
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