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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Essential spectrum for a Hilbert space operator

Author: Richard Bouldin
Journal: Trans. Amer. Math. Soc. 163 (1972), 437-445
MSC: Primary 47.30
Erratum: Trans. Amer. Math. Soc. 199 (1974), 429.
MathSciNet review: 0284837
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Abstract: Various notions of essential spectrum have been defined for densely defined closed operators on a Banach space. This paper shows that the theory for those notions of essential spectrum simplifies if the underlying space is a Hilbert space and the operator is reduced by its finite-dimensional eigenspaces. In that situation this paper classifies each essential spectrum in terms of the usual language for the spectrum of a Hilbert space operator. As an application this paper deduces the main results of several recent papers dealing with generalizations of the Weyl theorem.

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Keywords: Essential spectrum, operator on a Hilbert space, eigenvalue, algebraic multiplicity, geometric multiplicity, Fredholm operator, index, closed range
Article copyright: © Copyright 1972 American Mathematical Society