A class of (2m-1)-weakly amenable Banach algebras

Subject Areas : Functional analysis

M. Yegan ¹ (Department of Mathematics, Faculty of Basic Sciences, Imam Ali University, Tehran, Iran)

Received: 2021-07-30 Accepted : 2021-10-07 Published : 2021-09-01

Keywords: Banach algebras, cohomology group, weakly amenable,

Abstract :

‎Let ${\A}$ be a Banach space and ${\lambda}$ be a non-zero fixed element of ${\A}^{\ast}$(dual space of ${\A}$) with non-zero kernel‎. ‎Defining algebra product in $\A$ as $a\cdot b=\lambda(a)b$ for $a,b\in {\A}$‎, ‎we show that ${\A}$ is a $(2m-1)$-weakly amenable Banach algebra but not $2m$-weakly amenable for any $m\in{\N}$‎. ‎Furthermore‎, ‎we show the converse of the statement [2,~Proposition\,1.4.(ii)] ``for a non-unital Banach algebra $\A$‎, ‎if $\A$ is weakly amenable then $\A^{\#}$ is weakly amenable‎" ‎does not hold‎.

References:

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