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The stability radius of a quasi-Fredholm operator
Authors:Pak Wai Poon
Institution:Department of Mathematics, University of Melbourne, Victoria, 3052, Australia
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.

Keywords:Stability radius  Apostol spectrum  semi-regular  quasi-Fredholm operators  ascent  descent
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