Cyclic Module Amenability of Banach Algebras

Abstract

‎In this paper‎, ‎we define the concept of cyclic module amenability for Banach algebras and we study the hereditary properties of cyclic module amenability on Banach algebras‎. ‎For example‎, ‎we investigate relationship between cyclic module amenability of $I$‎, ‎$A/I$ and $A$‎, ‎where $I$ is closed ideal and $\mathfrak{A}$-submodule of $A$‎. ‎Also it is shown that cyclic module amenability of $A$ and $B$ follows from cyclic module amenability of $A\oplus_{\ell^1} B$ and cyclic module amenability of $A$ and $B$ implies cyclic module amenability of $A\oplus_{\ell^1} B$‎, ‎if $A$ and $B$ are essential.