The Banach algebras AC(𝜎) and BV(𝜎) - Doust, Ian; Leinert, Michael; Stoneham, Alan (Results in mathematics, 2023)
The spaces BV(𝜎) and AC(𝜎) were introduced as part of a program to find a general theory which covers both well-bounded operators and trigonometrically well-bounded operators acting on a Banach space. Since their initial appearance it has become clear that the definitions could be simplified somewhat. In this paper we give a self-contained exposition of the main properties of these spaces using this simplified approach.