A class of (2m-1)-weakly amenable Banach algebras
الموضوعات :
1 - Department of Mathematics, Faculty of Basic Sciences, Imam Ali University, Tehran, Iran
الکلمات المفتاحية: Banach algebras, cohomology group, weakly amenable,
ملخص المقالة :
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.
[1] F. F. Bonsall, J. Duncan, Complete Normed Algebras, Springer-Verlag, 1973.
[2] H. G. Dales, F. Ghahramani, N. Gronbæk, Derivations into iterated duals of Banach algebras, Studia Mathematica. 128 (1) (1998), 19-54.
[3] Y. Zhang, Weak amenability of a class of Banach algebras, Canad. Math. Bull. 44 (4) (2001), 504-508.
