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Spectral Theory and Differential Operators$
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David Edmunds and Des Evans

Print publication date: 2018

Print ISBN-13: 9780198812050

Published to Oxford Scholarship Online: September 2018

DOI: 10.1093/oso/9780198812050.001.0001

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Essential Spectra

Essential Spectra

(p.421) 9 Essential Spectra
Spectral Theory and Differential Operators

D. E. Edmunds

W. D. Evans

Oxford University Press

In this chapter, various essential spectra are studied. For a closed operator in a Banach space, a number of different sets have been used for the essential spectrum, the sets being identical for a self-adjoint operator in a Hilbert space. As well as the essential spectra, the changes that occur when the operator is perturbed are discussed. Constant-coefficient differential operators are studied in detail.

Keywords:   essential spectrum, singular sequence, T-compact perturbation, compact resolvent, finite-dimensional extension, direct and orthogonal sums

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