Module super-amenability for semigroup algebras

2009/12/23 by Abasalt Bodaghi, Bodaghi, Abasalt, Massoud Amini +1
Computer Science · Mathematics · #46H25 #Advanced Algebra and Logic #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:46H25 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.0912.4624

9 pages

arxiv created 2009/12/23 · openalex publication_date 2009/12/23 · arxiv updated 2010/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let S be an inverse semigroup with the set of idempotents E. In this paper we define the module super-amenability of a Banach algebra which is a Banach module over another Banach algebra with compatible actions, and show that when E is upward directed and acts on S trivially from left and by multiplication from right, the semigroup algebra ℓ ¹(S) is ℓ¹(E)-module super-amenable if and only if an appropriate group homomorphic image of S is finite.

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