Weak amenability of the Lau product of Banach algebras defined by a Banach algebra morphism.

*(English)*Zbl 1423.46068Summary: 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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\textit{M. Ramezanpour}, Bull. Korean Math. Soc. 54, No. 6, 1991--1999 (2017; Zbl 1423.46068)

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##### References:

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