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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.
##### Keywords:
Banach algebra; derivation; weak amenability; $$T$$-Lau product
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##### References:
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