Module amenability of the second dual and module topological center of semigroup algebras

Let $S$ be an inverse semigroup with an upward directed set of idempotents $E$. In this paper we define the module topological center of second dual of a Banach algebra which is a Banach module over another Banach algebra with compatible actions, and find it for $\ell ^{1}(S)^{**}$ (as an $\ell^{1}(E)$-module). We also prove that $\ell ^{1}(S)^{**}$ is $\ell^{1}(E)$-module amenable if and only if an appropriate group homomorphic image of $S$ is finite.

No reviews yet.

No comments yet.