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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

The Fredholm radius of a bundle of closed linear operators


Author: E.-O. Liebetrau
Journal: Proc. Amer. Math. Soc. 70 (1978), 67-71
MSC: Primary 47B30
DOI: https://doi.org/10.1090/S0002-9939-1978-0477858-1
MathSciNet review: 0477858
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Abstract: Given a bundle of linear operators $ T - \lambda S$, where T is closed and S is bounded, a sequence $ \{ {\delta _m}(T:S)\} $ of extended real numbers is defined. If T is a Fredholm operator, the limit $ {\lim \delta _m}{(T:S)^{1/m}}$ exists and is equal to the supremum of all $ r > 0$ such that $ T - \lambda S$ is a Fredholm operator for $ \vert\lambda \vert < r$.


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DOI: https://doi.org/10.1090/S0002-9939-1978-0477858-1
Keywords: Fredholm operators, perturbation theory
Article copyright: © Copyright 1978 American Mathematical Society