Ian Doust's information pages

AC(σ) operators

Journal of Operator Theory, 65 (2011), 255-279.

Brenden Ashton and Ian Doust

Address: School of Mathematics, University of New South Wales, Sydney NSW 2052, Australia

Email:  i.doust@unsw.edu.au

Abstract: In this paper we present a new extension of the theory of well-bounded operators to cover operators with complex spectrum. In previous work a new concept of the class of absolutely continuous functions on a nonempty compact subset σ of the plane, denoted AC(σ), was introduced. An AC(σ) operator is one which admits a functional calculus for this algebra of functions. The class of AC(σ) operators includes all of the well-bounded operators and trigonometrically well-bounded operators, as well as all scalar-type spectral operators, but is strictly smaller than Berkson and Gillespie's class of AC operators. This paper develops the spectral properties of AC(σ) operators and surveys some of the problems which remain in extending results from the theory of well-bounded operators.

Note: The final version of the paper may differ from the manuscript below. This paper is also available on the arXiv.

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