Relative amenability of Banach algebras

TL;DR

This paper introduces and explores the concept of relative amenability in Banach algebras, analyzing its properties and implications for triangular algebras and group-related algebras, extending Johnson's theorem.

Contribution

It generalizes Johnson's theorem through the framework of relative amenability, providing new insights into the structure of Banach algebras and their ideals.

Findings

Established conditions for relative amenability in various Banach algebra classes

Extended Johnson's theorem to the context of relative amenability

Analyzed the relative amenability of triangular and group-related 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.