Weak and $(-1)$-weak amenability of second dual of Banach algebras

Document Type : Research Paper


1 University of Simon Fraser, Department of Education, Vancouver, Canada

2 University of Arkansas, Department of Mathematical sciences, Fayetteville, AR 72703, USA


For a Banach algebra $A$, $A''$ is $(-1)$-Weakly amenable if $A'$ is a Banach $A''$-bimodule and $H^1(A'',A')=\{0\}$. In this paper, among other things,  we study the relationships between the $(-1)$-Weakly amenability of $A''$ and the weak amenability of $A''$ or $A$. Moreover, we show that the second dual of every $C^\ast$-algebra is $(-1)$-Weakly amenable.