Generalized Module Extension Banach Algebras: Derivations and Weak Amenability

Mohammad Ramezanpour, Seddigheh Barootkoob

Let $A$ and $X$ be Banach algebras and let $X$ be an algebraic Banach $A-$module. Then the ${\ell }^1-$direct sum $A\times X$ equipped with the multiplication $$(a,x)(b,y)=(ab, ay+xb+…