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On the spectrum of a linear operator

Published online by Cambridge University Press:  18 May 2009

Michael B. Dollinger  and
Kirti K. Oberai
Michael B. Dollinger
Affiliation:
Louisiana State University, Baton Rouge, Louisiana
Kirti K. Oberai
Affiliation:
Queen's University, Kingston, Ontario
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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.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 13 , Issue 2 , September 1972 , pp. 98 - 101
Copyright
Copyright © Glasgow Mathematical Journal Trust 1972

References

REFERENCES

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