Weak amenability of the Lau product of Banach algebras defined by a Banach algebra morphism
Bull. Korean Math. Soc. 2017 Vol. 54, No. 6, 1991-1999
Published online July 13, 2017
Printed November 30, 2017
Mohammad Ramezanpour
Damghan University
Abstract : Let $A$ and $B$ be two Banach algebras and $T:B\to A$ be a bounded homomorphism, with $\|T\|\leq 1$. Recently, Dabhi, Jabbari and Haghnejad Azar (\textit{Acta Math. Sin. $($Engl. Ser.$)$} \textbf{31} (2015), no. 9, 1461--1474) 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 $n\geq0$.
Keywords : Banach algebra, derivation, weak amenability, $T$-Lau product
MSC numbers : 46H05, 47B47
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