Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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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.

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

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