Semigroup Forum

, Volume 80, Issue 2, pp 302–312 | Cite as

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

  • Massoud Amini
  • Abasalt Bodaghi
  • Davood Ebrahimi Bagha
Research Article

Abstract

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 1(S)**, as an 1(E)-module, for an inverse semigroup S with an upward directed set of idempotents E. We also prove that 1(S)** is 1(E)-module amenable if and only if an appropriate group homomorphic image of S is finite.

Keywords

Banach modules Module derivation Module amenability Module topological center Inverse semigroup 

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Massoud Amini
    • 1
  • Abasalt Bodaghi
    • 2
  • Davood Ebrahimi Bagha
    • 3
  1. 1.Department of Mathematics, Faculty of Mathematical SciencesTarbiat Modares UniversityTehranIran
  2. 2.Islamic Azad University, Garmsar BranchGarmsarIran
  3. 3.Islamic Azad University, Central Tehran BranchTehranIran

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