Ascent, descent, and commuting perturbations

Kaashoek, M. A.; Lay, D. C.

doi:10.1090/S0002-9947-1972-0312299-8

Ascent, descent, and commuting perturbations
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by M. A. Kaashoek and D. C. Lay

Trans. Amer. Math. Soc. 169 (1972), 35-47

DOI: https://doi.org/10.1090/S0002-9947-1972-0312299-8

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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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