Functions of bounded variation on compact subsets of the plane
Volume 169 / 2005
Studia Mathematica 169 (2005), 163-188
MSC: 47B40, 26B30.
DOI: 10.4064/sm169-2-5
Abstract
A major obstacle in extending the theory of well-bounded operators to cover operators whose spectrum is not necessarily real has been the lack of a suitable variation norm applicable to functions defined on an arbitrary nonempty compact subset $\sigma$ of the plane. In this paper we define a new Banach algebra ${\rm BV}(\sigma)$ of functions of bounded variation on such a set and show that the function-theoretic properties of this algebra make it better suited to applications in spectral theory than those used previously.
