Document Type : Research Paper

Authors

• Mohammad Hossein Sattari
• Hamid Shafieasl

Department of Mathematics, Faculty of Science, Azarbaijan Shahid Madani University, P.O.Box 53751-71379, Tabriz, Iran.

Abstract

In 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 $\ell^1(S)$ is  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.

Keywords

• Banach algebras
• Symmetric amenability
• Module amenability

Main Subjects

• Banach Algebra