Mathematics – Functional Analysis
Scientific paper
2009-12-20
Mathematics
Functional Analysis
9 pages
Scientific paper
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.
Amini Massoud
Bagha Davood Ebrahimi
Bodaghi Abasalt
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