Characterization of SAR Banach algebras beyond known classes

Identify Banach algebras with stable Arens regularity that are neither Banach function algebras nor C*-algebras.

Background

Stable Arens regularity is introduced as a property ensuring that sufficiently small perturbations of an Arens-regular Banach algebra remain Arens regular. The paper proves this property for Banach function algebras equivalent to uniform algebras and cites its validity for C*-algebras.

The authors explicitly seek further examples outside these two established classes. The problem therefore asks for construction or identification of additional Banach algebras whose Arens regularity is stable under sufficiently small perturbations.