Spectral value sets of closed linear operators
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 1364-5021Full text not available from this repository.
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|
|Journal or Publication Title:||PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES|
|Publisher:||ROYAL SOC LONDON|
|Official Date:||8 June 2000|
|Number of Pages:||22|
|Page Range:||pp. 1397-1418|
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