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

 

The stability radius
of a quasi-Fredholm operator


Author: Pak Wai Poon
Journal: Proc. Amer. Math. Soc. 126 (1998), 1071-1080
MSC (1991): Primary 47A55, 47A10, 47A53
MathSciNet review: 1443849
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Abstract: We extend the technique used by Kordula and Müller to show that the stability radius of a quasi-Fredholm operator $T$ is the limit of $\gamma(T^n)^{1/n}$ as $n\rightarrow\infty$. If $0$ is an isolated point of the Apostol spectrum $\sigma _\gamma(T)$, then the above limit is non-zero if and only if $T$ is quasi-Fredholm.


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Additional Information

Pak Wai Poon
Affiliation: Department of Mathematics, University of Melbourne, Victoria, 3052, Australia
Email: pakpoon@maths.mu.oz.au

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04253-1
PII: S 0002-9939(98)04253-1
Keywords: Stability radius, Apostol spectrum, semi-regular, quasi-Fredholm operators, ascent, descent
Received by editor(s): June 21, 1996
Received by editor(s) in revised form: September 23, 1996
Additional Notes: The results in this paper form a part of the author’s research for the degree of Ph.D. at the University of Melbourne, 1996, under the supervision of J. J. Koliha.
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1998 American Mathematical Society