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Über das wachstum von resolventen in der nähe einer isolierten singularität

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Abstract

Let L(λ) be a bundle of linear bounded operators between two Banach spaces. In this paper we study the behaviour of {L(λ)}−1, if λ tends to λo and L(λo) is a Fredholm operator with index 0. We show that the growth of this resolvent can be described by the length of certain chains of generalized principal vectors; if L(λ) depends analytically on the parameter λ, we get a complete characterization for an isolated singularity of L, and also a Laurent expansion for the resolvent. Finally, we give applications to a broad class of bundles of bounded self-adjoint operators.

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  1. Institut für Angewandte, Mathematik der Universität, Kaiserstraβe 27, D-87, Würzburg

    Paul Sarreither

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  1. Paul Sarreither
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Sarreither, P. Über das wachstum von resolventen in der nähe einer isolierten singularität. Manuscripta Math 11, 261–272 (1974). https://doi.org/10.1007/BF01173717

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  • DOI: https://doi.org/10.1007/BF01173717

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