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Variation of discrete spectra

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Abstract

A formula [see (1) below] estimating collectively the variation of eigenvalues of a symmetric matrix under a perturbation is extended to the case of discrete eigenvalues of a selfadjoint operator in Hilbert space, under the assumption that the perturbation is compact. For this purpose, the notion of an extended enumeration of discrete eigenvalues is introduced.

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Reference

  1. Kato, T.: Perturbation theory for linear operators. Berlin, Heidelberg, New York: Springer 1966, 1984

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Authors and Affiliations

  1. Department of Mathematics, University of California, 94720, Berkeley, CA, USA

    Tosio Kato

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  1. Tosio Kato
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Communicated by B. Simon

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Kato, T. Variation of discrete spectra. Commun.Math. Phys. 111, 501–504 (1987). https://doi.org/10.1007/BF01238911

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  • DOI: https://doi.org/10.1007/BF01238911

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