a class of (2m-1)-weakly amenable banach algebras

‎let ${a}$ be a banach space and ${lambda}$ be a nonzero fixed element of ${a}^{ast}$(dual space of ${a}$) with nonzero kernel‎. ‎defining algebra product in $a$ as $acdot b=lambda(a)b$ for $a,bin {a}$‎, ‎we show that ${a}$ is a $(2m1)$weakly amenable banach algebra but not $2m$weakly amenable for any $min{n}$‎. ‎furthermore‎, ‎we show the converse of the statement [2,~proposition,1.4.(ii)] ``for a nonunital banach algebra $a$‎, ‎if $a$ is weakly amenable then $a^{#}$ is weakly amenable‎ ‎does not hold‎.