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A COMPARISON OF ALGEBRAS OF FUNCTIONS OF BOUNDED VARIATION

Published online by Cambridge University Press:  25 January 2007

Brenden Ashton  and
Ian Doust
Brenden Ashton
Affiliation:
Canon Information Systems Research Australia, 3 Thomas Holt Drive, North Ryde, NSW 2113, Australia ([email protected])
Ian Doust
Affiliation:
School of Mathematics, University of New South Wales, Sydney, NSW 2052, Australia ([email protected])
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Abstract

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Motivated by problems in the spectral theory of linear operators, we previously introduced a new concept of variation for functions defined on a non-empty compact subset of the plane. In this paper, we examine the algebras of functions of bounded variation one obtains from these new definitions for the case where the underlying compact set is either a rectangle or the unit circle, and compare these algebras with those previously used by Berkson and Gillespie in their theories of AC-operators and trigonometrically well-bounded operators.

Keywords

Primary 47B4026B30functions of bounded variationabsolutely continuous functionsfunctional calculuswell-bounded operatorsAC-operators
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 49 , Issue 3 , October 2006 , pp. 575 - 591
Copyright
Copyright © Edinburgh Mathematical Society 2006