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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A generalization of the punctured neighborhood theorem


Author: Woo Young Lee
Journal: Proc. Amer. Math. Soc. 117 (1993), 107-109
MSC: Primary 47A10
DOI: https://doi.org/10.1090/S0002-9939-1993-1113645-7
MathSciNet review: 1113645
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Abstract: If $ T \in \mathcal{L}(X)$ is regular on a Banach space $ X$, with finite- dimensional intersection $ {T^{ - 1}}(0) \cap T(X)$, and if $ S,\;S'$ are invertible, commute with $ T$ and have sufficiently small norm, then $ \dim {(T - S')^{ - 1}}(0) = \dim {(T - S)^{ - 1}}(0)$ and $ \dim X/(T - S')X = \dim X/(T - S)X$.


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DOI: https://doi.org/10.1090/S0002-9939-1993-1113645-7
Keywords: Punctured neighborhood theorem, regular operators, spectrum
Article copyright: © Copyright 1993 American Mathematical Society