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On the spectrum of a linear operator
Published online by Cambridge University Press: 18 May 2009
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In the definition of the spectrum of a linear operator, it is customary to assume that the underlying space is complete. However there are occasions for which it is neither desirable nor necessary to assume completeness in order to obtain a spectral theory for an operator; for example, completeness is not needed in the Riesz theory of a compact operator (see e.g. [1: XI. 3]). Several non-equivalent definitions for the spectrum of an operator on normed spaces have appeared in the literature. We shall discuss the relationship among these definitions and some of the difficulties that arise in applying these definitions to obtain a spectral theory.
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- Copyright © Glasgow Mathematical Journal Trust 1972
References
REFERENCES
2.Neubauer, G., Zur Spektraltheorie in lokalconvexen Algebren, Math. Ann. 142 (1961), 131–164.Google Scholar
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5.West, T. T., Operators with a single spectrum, Proc. Edinburgh Math. Soc. (2) 15 (1966), 11–18.Google Scholar
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