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Weak amenability of the Lau product of Banach algebras defined by a Banach algebra morphism. (English) Zbl 1423.46068
Summary: Let \(A\) and \(B\) be two Banach algebras and \(T:B\to A\) be a bounded homomorphism, with \(\|T\|\leq 1\). Recently, P. A. Dabhi et al. [Acta Math. Sin., Engl. Ser. 31, No. 9, 1461–1474 (2015; Zbl 1335.46040)] obtained some results about the \(n\)-weak amenability of \(A\times_T B\). In the present paper, we address a gap in the proof of these results and extend and improve them by discussing general necessary and sufficient conditions for \(A\times_T B\) to be \(n\)-weakly amenable, for an integer \(n\geq0\).

MSC:
46H05 General theory of topological algebras
46H25 Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)
47B47 Commutators, derivations, elementary operators, etc.
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