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Spectral value sets of closed linear operators
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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 | ||||
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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 | ||||
Official Date: | 8 June 2000 | ||||
Dates: |
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Volume: | 456 | ||||
Number: | 1998 | ||||
Number of Pages: | 22 | ||||
Page Range: | pp. 1397-1418 | ||||
Publication Status: | Published |
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