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 σ of the plane. In this paper we define a new Banach algebra BV(σ) 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm169-2-5,
author = {Brenden Ashton and Ian Doust},
title = {Functions of bounded variation on compact subsets of the plane},
journal = {Studia Mathematica},
volume = {166},
year = {2005},
pages = {163-188},
zbl = {1071.47034},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm169-2-5}
}
Brenden Ashton; Ian Doust. Functions of bounded variation on compact subsets of the plane. Studia Mathematica, Tome 166 (2005) pp. 163-188. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm169-2-5/