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Approximate weak amenability of extension Banach algebras. (English) Zbl 1371.46039

Summary: The aim of this paper is to display sufficient conditions on Banach algebras without bounded approximate identity such that every continuous derivation is approximately inner. We apply these results to prove weak amenability of Banach algebras and approximate \(n\)-weak amenability of extension Banach algebras.

MSC:

46H25 Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)
46H20 Structure, classification of topological algebras
46H35 Topological algebras of operators
47B47 Commutators, derivations, elementary operators, etc.
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