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Essential Spectrum for a Hilbert Space Operator

Richard Bouldin
Transactions of the American Mathematical Society
Vol. 163 (Jan., 1972), pp. 437-445
DOI: 10.2307/1995731
Stable URL: http://www.jstor.org/stable/1995731
Page Count: 9
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Essential Spectrum for a Hilbert Space Operator
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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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