Proceedings of the American Mathematical Society

Author(s): Pak Wai Poon
Journal: Proc. Amer. Math. Soc. 126 (1998), 1071-1080.
MSC (1991): Primary 47A55, 47A10, 47A53
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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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Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 47A55, 47A10, 47A53

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

DOI: 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
Copyright of article: Copyright 1998, American Mathematical Society

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