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Approximating Fredholm operators on a nonseparable Hilbert space

Published online by Cambridge University Press:  18 May 2009

Richard Bouldin
Richard Bouldin
Affiliation:
Department of MathematicsUniversity of GeorgiaAthensGeorgia 30602U.S.A.
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Abstract

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This paper obtains a simple formula for the distance from a given operator to the set of invertible operators without requiring the underlying space to be separable. That formula is used to compute the distance to the Fredholm operators with a given index. These results require the further study of the concepts of essential nullity and essential deficiency, which permitted us to characterize the closure of the invertible operators. We also introduce a parameter called the modulus of Fredholmness.

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 35 , Issue 2 , May 1993 , pp. 167 - 178
Copyright
Copyright © Glasgow Mathematical Journal Trust 1993

References

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