The stability radius of a quasi-Fredholm operator

Poon, Pak

doi:10.1090/S0002-9939-98-04253-1

The stability radius of a quasi-Fredholm operator
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by Pak Wai Poon

Proc. Amer. Math. Soc. 126 (1998), 1071-1080

DOI: https://doi.org/10.1090/S0002-9939-98-04253-1

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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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