Perturbations of Banach algebras and amenability

TL;DR

This paper demonstrates that small perturbations of the multiplication in an amenable Banach algebra preserve its amenability, establishing stability under certain bounded changes.

Contribution

It introduces a quantitative condition under which the amenability of a Banach algebra is maintained despite perturbations of its multiplication.

Findings

Amenability is stable under perturbations less than 1/11 in the algebra's multiplication.

Provides a specific bound for the perturbation size that preserves amenability.

Extends understanding of structural stability in Banach algebras.

Abstract

In this paper we prove that if (A,\pi) is an amenable Banach algebra and if \rho is another Banach algebra multiplication on A such that the difference between \rho and and \pi is less than 1/11, then (A, \rho) is also amenable.