The Banach algebras $AC(\sigma )$ and $BV(\sigma )$

Abstract

The spaces $BV(\sigma )$ and $AC(\sigma )$ 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.

33 pages. Some material previously appeared in an earlier version of arxiv:1312.1806