Module symmetrically amenable Banach algebras

Inceboz, Hulya and Arslan, Berna and Bodaghi, Abasalt (2017) Module symmetrically amenable Banach algebras. ACTA MATHEMATICA ACADEMIAE PAEDAGOGICAE NYÍREGYHÁZIENSIS, 33 (2). pp. 233-245. ISSN 0866-0174

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Abstract

In this article, we develop the concept of symmetric amenability for a Banach algebra A to the case that there is an extra A-module structure on A. For every inverse semigroup S with the set E of idempotents, we find necessary and sufficient conditions for the l 1 (S) to be module symmetrically amenable (as a l 1 (E)-module). We also present some module symmetrically amenable semigroup algebras to show that this new notion of amenability is different from the classical case introduced by Johnson.

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