University of MaraghehSahand Communications in Mathematical Analysis2322-580705120170101Symmetric module and Connes amenability49592138210.22130/scma.2017.21382ENMohammad HosseinSattariDepartment of Mathematics, Faculty of Science, Azarbaijan Shahid Madani University, P.O.Box 53751-71379, Tabriz, Iran.HamidShafieaslDepartment of Mathematics, Faculty of Science, Azarbaijan Shahid Madani University, P.O.Box 53751-71379, Tabriz, Iran.Journal Article20160515In this paper we introduce two symmetric variants of amenability, symmetric module amenability and symmetric Connes amenability. We determine symmetric module amenability and symmetric Connes amenability of some concrete Banach algebras. Indeed, it is shown that $ell^1(S)$ isĀ a symmetric $ell^1(E)$-module amenable if and only if $S$ is amenable, where $S$ is an inverse semigroup with subsemigroup $E(S)$ of idempotents. In symmetric connes amenability, we have proved that $M(G)$ is symmetric connes amenable if and only if $G$ is amenable.https://scma.maragheh.ac.ir/article_21382_4d0846371eaab14fedda80b8067ab743.pdf