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

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

2009-12-20

arxiv.org/abs/0912.4003v2

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.

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