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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

On a generalized punctured neighborhood theorem in $ \mathcal{L}(X)$


Author: Christoph Schmoeger
Journal: Proc. Amer. Math. Soc. 123 (1995), 1237-1240
MSC: Primary 47A53; Secondary 47A10
MathSciNet review: 1211590
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Abstract: Suppose that T is a bounded linear operator on a complex Banach space X. If $ {T^2}(X)$ is closed, $ T(X) \cap N(T)$ is finite dimensional, and S is a bounded linear operator on X such that S is invertible, commutes with T, and has sufficiently small norm, then $ T - S$ is upper semi-Fredholm.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1211590-1
PII: S 0002-9939(1995)1211590-1
Keywords: Semi-Fredholm operator, spectrum, essential spectrum
Article copyright: © Copyright 1995 American Mathematical Society