Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 33, No. 2, pp. 233-245 (2017)

Module symmetrically amenable Banach algebras

Hulya Inceboz, Berna Arslan and Abasalt Bodaghi

Adnan Menderes University and Islamic Azad University

Abstract: In this article, we develop the concept of symmetric amenability for a Banach algebra $\mathcal A$ to the case that there is an extra $\mathfrak A$-module structure on $\mathcal A$. 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.

Keywords: Banach modules, module symmetric amenability, semigroup algebra, inverse semigroup

Classification (MSC2000): 46H25; 43A07

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