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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Ascent, descent, and commuting perturbations
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by M. A. Kaashoek and D. C. Lay PDF
Trans. Amer. Math. Soc. 169 (1972), 35-47 Request permission

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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Additional Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 169 (1972), 35-47
  • MSC: Primary 47A55
  • DOI: https://doi.org/10.1090/S0002-9947-1972-0312299-8
  • MathSciNet review: 0312299