Some cohomological properties of Banach algebras

Abstract

In this manuscript, we investigate and study some cohomological  properties of  Banach algebras. Let $A$ be a Banach algebra with left bounded approximate identity, and let  $B$ be a Banach $A-bimodule$.  We show that if $AB^{**}$ and $B^{**}A$ are subset of $B$, then  $H^1(A,B^{(2n+1)})=0$ for all $n\geq 0$, whenever $H^1(A,B^*)=0$.