Arens regularity of module actions and weak amenability of Banach algebras (Q313478)

The authors give some results concerning criteria of Arens regularity of Banach algebras in the sense of \textit{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 \textit{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.