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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Ascent, descent, and commuting perturbations

Authors: M. A. Kaashoek and D. C. Lay
Journal: Trans. Amer. Math. Soc. 169 (1972), 35-47
MSC: Primary 47A55
MathSciNet review: 0312299
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Abstract: In the present paper we investigate the stability of the ascent and descent of a linear operator $ T$ when $ T$ is subjected to a perturbation by a linear operator $ C$ which commutes with $ T$. The domains and ranges of $ T$ and $ C$ lie in some linear space $ X$. The results are used to characterize the Browder essential spectrum of $ T$. We conclude with a number of remarks concerning the notion of commutativity used in the present paper.

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Keywords: Ascent, descent, finite-dimensional perturbations, compact perturbations, Riesz operators, Browder essential spectrum, commuting operators
Article copyright: © Copyright 1972 American Mathematical Society