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Differentiable perturbation of unbounded operators

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Abstract.

If A(t) is a C 1,α-curve of unbounded self-adjoint operators with compact resolvents and common domain of definition, then the eigenvalues can be parameterized C 1 in t. If A is C ∞ then the eigenvalues can be parameterized twice differentiably.

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Authors and Affiliations

  1. Institut für Mathematik, Universität Wien, Strudlhofgasse 4, A-1090, Wien, Austria

    Andreas Kriegl

  2. Erwin Schrödinger Institute of Mathematical Physics, Boltzmanngasse 9, A-1090, Wien, Austria

    Peter W. Michor

Authors
  1. Andreas Kriegl
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  2. Peter W. Michor
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Corresponding author

Correspondence to Andreas Kriegl.

Additional information

Mathematics Subject Classification (2000): 26C10

PWM was supported by FWF, Projekt P 14195 MAT.

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Kriegl, A., Michor, P. Differentiable perturbation of unbounded operators. Math. Ann. 327, 191–201 (2003). https://doi.org/10.1007/s00208-003-0446-5

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  • DOI: https://doi.org/10.1007/s00208-003-0446-5

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