Banach algebras of sequences of generalized bounded variation

Abstract

This article is to shed light on a class of commutative unital complex Banach algebras. We show that these Banach algebras of sequences of generalized bounded variation are all semi-simple, regular, and self-adjoint and that their carrier spaces are homeomorphic to compactifications of the discrete space of positive integers. In particular, we provide necessary and sufficient conditions under which the carrier space may be identified with the one-point compactification or the Stone–Čech compactification of the positive integers. It turns out that the carrier spaces of many of the Banach algebras under consideration are neither of these familiar compactifications.