A generalization of the \(n\)-weak amenability of Banach algebras. (English) Zbl 1224.46095

Summary: Let \(A\) be a Banach algebra and \(\varphi:A\to A\) be a continuous homomorphism. We generalize the notion of \(n\)-weak amenability of \(A\) to that of \((\varphi)\)-\(n\)-weak amenability for \(n\in\mathbb N\). We give conditions under which the module extension Banach algebra and second dual of \(A\) are \((\varphi)\)-\(n\)-weakly amenable.


46H20 Structure, classification of topological algebras
46H10 Ideals and subalgebras
46H25 Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)
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