Module amenability of Banach algebras and semigroup algebras

We define the concepts of the first and the second module dual of a Banach space $X$. And also bring a new concept of module amenability for a Banach algebra $\mathcal{A}$. For inverse semigroup $S$, we will give a new action for $\ell^1(S)$ as a Banach $\ell^1(E_S)$-module and show that if $S$ is amenable then $\ell^1(S)$ is $\ell^1(E_S)$-module amenable. KCI Citation Count: 0