Relative amenability of Banach algebras

Abstract

‎Let $A$ be a Banach algebra and $I$ be a closed ideal of $A$‎. ‎We say that $A$ is amenable relative to $I$‎, ‎if $A/I$ is an amenable Banach algebra‎. ‎We study the relative amenability of Banach algebras and investigate the relative amenability of triangular Banach algebras and Banach algebras associated to locally compact groups‎. ‎We generalize some of the previous known results by applying the concept of relative amenability of Banach algebras‎, ‎especially‎, ‎we present a generalization of Johnson's theorem in the concept of relative amenability‎.