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

By M. Amini, Abasalt Bodaghi, D. Ebrahimi Bagha. 2009

60 citations recorded by the source corpus.

In this paper we define the module topological center of the second dual $\mathcal{A}^{**}$ of a Banach algebra $\mathcal{A}$ which is a Banach $\mathfrak{A}$-module with compatible actions on another Banach algebra $\mathfrak{A}$. We calculate the module topological center of ℓ1(S)**, as an ℓ1(E)-module, for an inverse semigroup S with an upward directed set of idempotents E. We also prove that ℓ1(S)** is ℓ1(E)-module amenable if and only if an appropriate group homomorphic image of S is finite.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/13d2885052d9b384e34469c6dd418b1487d4602e