Bull. Korean Math. Soc. 2017; 54(6): 1991-1999
Online first article July 13, 2017 Printed November 30, 2017
https://doi.org/10.4134/BKMS.b160690
Copyright © The Korean Mathematical Society.
Mohammad Ramezanpour
Damghan University
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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