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A perturbation theorem for the essential spectral radius of strongly continuous semigroups

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Abstract

We generalize the Jörgens-Vidav semigroup perturbation theorem: If (U (t)), (V (t)) are s. c. semigroups, the generator of (V (t)) a bounded perturbation of the generator of (U (t)), and some remainder in the iteration series ofV (t) is strictly power compact, then the spectrum ofV (t) outside the spectral disc ofU (t) consists of eigenvalues of finite algebraic multiplicity. As a prerequisite, we show the invariance of components of the essential resolvent set of an operator under relatively power compact pertubations.

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  1. Mathematisches Institut, Ludwig-Maximilian-Universität München, Theresienstraße 39, D-8000, München 2, Germany

    Jürgen Voigt

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  1. Jürgen Voigt
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Voigt, J. A perturbation theorem for the essential spectral radius of strongly continuous semigroups. Monatshefte für Mathematik 90, 153–161 (1980). https://doi.org/10.1007/BF01303264

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  • DOI: https://doi.org/10.1007/BF01303264

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