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Module Amenability for Semigroup Algebras

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Abstract

We extend the concept of amenability of a Banach algebra A to the case that there is an extra \A-module structure on A, and show that when S is an inverse semigroup with subsemigroup E of idempotents, then A = \ell1(S) as a Banach module over \A = \ell1(E) is module amenable if and only if S is amenable. When S is a discrete group, \ell1(E) = ℂ and this is just the Johnson’s theorem.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Saskatchewan, 106 Wiggins Road, Saskatoon, Saskatchewan, S7N 5E6, Canada and (Permanent address) Department of Mathematics, Tarbiat Modarres University, P.O. Box 14115-175, Tehran, Iran

    Massoud Amini

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  1. Massoud Amini
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Correspondence to Massoud Amini.

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Amini, M. Module Amenability for Semigroup Algebras. Semigroup Forum 69, 243–254 (2004). https://doi.org/10.1007/s00233-004-0107-3

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  • DOI: https://doi.org/10.1007/s00233-004-0107-3

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