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A note on the punctured neighbourhood theorem

Published online by Cambridge University Press:  18 May 2009

Robin Harte  and
Woo Young Leef
Robin Harte
Affiliation:
School of Mathematics, Trinity College, Dublin 2, Ireland
Woo Young Leef
Affiliation:
Department of Mathematics, Sung Kwan University, Suwon 440–746, Korea
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The punctured neighbourhood theorem an be interpreted as saying that if 0 ∈ C is on the boundary of the spectrum of a Fredholm operator then it must be an isolated point of that spectrum. This extends to semi-Fredholm operators, in particular to operators with closed range and finite dimensional null space. In this note we generalise both the finite dimensionality of the null space and the scalars involved in the definition of an isolated point of the spectrum.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 39 , Issue 3 , September 1997 , pp. 269 - 273
Copyright
Copyright © Glasgow Mathematical Journal Trust 1997

References

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