UNSPECIFIED (2000) Spectral value sets of closed linear operators. PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 456 (1998). pp. 1397-1418. ISSN 1364-5021

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Abstract

We study how the spectrum of a closed linear operator on a complex Banach space changes under affine perturbations of the form A curved right arrow A(Delta) = A + D Delta E. Here A, D and E are given linear operators, whereas Delta is an unknown bounded linear operator that parametrizes the possibly unbounded perturbation D Delta E. The union of the spectra of the perturbed operators A(Delta), with the norm of Delta smaller than a given delta > 0, is called the spectral value set of A at level delta. In this paper we extend a known characterization of these sets for the matrix case to infinite dimensions, and in so doing present a framework that allows for unbounded perturbations of closed linear operators on Banach spaces. The results will be illustrated by applying them to a delay system with uncertain parameters and to a partial differential equation with a perturbed boundary condition.

Item Type:	Journal Article
Subjects:	Q Science
Journal or Publication Title:	PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
Publisher:	ROYAL SOC LONDON
ISSN:	1364-5021
Date:	8 June 2000
Volume:	456
Number:	1998
Number of Pages:	22
Page Range:	pp. 1397-1418
Publication Status:	Published
URI:	http://wrap.warwick.ac.uk/id/eprint/13279

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