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Über nichtlineare Spektral- und Störungstheorie

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Abstract

A topology is defined on the set of closed operators between two Banach spaces. We show that the set of Lipschitzcontinuous operators is open in this topology; the relative topology on this subset is the natural one. The notion of spectrum is defined for nonlinear maps, and we prove among others the following facts: the resolvent set is open and depends upper semi-continuously on the operator; for Lipschitzcontinuous operators, the spectrum is compact; the resolvent map is continuous. Then we examine more closely the cases of Fréchet-differentiable maps and of isolated points in the spectrum.

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Authors and Affiliations

  1. Mathematisches Institut der Universität zu Köln, Weyertal 86-90, BRD-5, Köln 41

    Wilhelm Singhof

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  1. Wilhelm Singhof
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Diese Arbeit ist eine gekürzte Version der beim Fachbereich Mathematik der Universität Mainz vorgelegten Doktorarbeit des Verfassers.

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Singhof, W. Über nichtlineare Spektral- und Störungstheorie. Manuscripta Math 14, 123–162 (1974). https://doi.org/10.1007/BF01171438

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  • DOI: https://doi.org/10.1007/BF01171438

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