Mathematische Annalen

, Volume 353, Issue 2, pp 519–522 | Cite as

Many parameter Hölder perturbation of unbounded operators



If \({u \mapsto A(u)}\) is a C 0,α -mapping, for 0 < α ≤ 1, having as values unbounded self-adjoint operators with compact resolvents and common domain of definition, parameterized by u in an (even infinite dimensional) space, then any continuous (in u) arrangement of the eigenvalues of A(u) is indeed C 0,α in u.

Mathematics Subject Classification (2000)

Primary 47A55 47A56 47B25 


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  1. 1.
    Bhatia R.: Matrix analysis, graduate texts in mathematics, vol. 169. Springer, New York (1997)Google Scholar
  2. 2.
    Boman J.: Differentiability of a function and of its compositions with functions of one variable. Math. Scand. 20, 249–268 (1967)MathSciNetMATHGoogle Scholar
  3. 3.
    Dieudonné J.: Foundations of modern analysis, Pure and Applied Mathematics, vol. X. Academic Press, New York (1960)Google Scholar
  4. 4.
    Faure C.-A.: Sur un théorème de Boman. C. R. Acad. Sci. Paris Sér. I Math. 309(20), 1003–1006 (1989)MathSciNetMATHGoogle Scholar
  5. 5.
    Faure, C.-A.: Théorie de la différentiation dans les espaces convenables. Ph.D. thesis, Université de Genéve (1991)Google Scholar
  6. 6.
    Faure C.-A., Frölicher A.: Hölder differentiable maps and their function spaces, categorical topology and its relation to analysis, algebra and combinatorics (Prague, 1988), pp. 135–142. World Science Publishers, Teaneck (1989)Google Scholar
  7. 7.
    Frölicher A., Kriegl A.: Linear spaces and differentiation theory, pure and applied mathematics (New York). John Wiley & Sons Ltd., A Wiley-Interscience Publication, Chichester (1988)Google Scholar
  8. 8.
    Kriegl, A., Michor, P.W.: The convenient setting of global analysis, mathematical surveys and monographs, vol. 53. American Mathematical Society, Providence, RI, USA (1997).
  9. 9.
    Kriegl A., Michor P.W.: Differentiable perturbation of unbounded operators. Math. Ann. 327(1), 191–201 (2003)MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    Weyl H.: Das asymptotische Verteilungsgesetz der Eigenwerte linearer partieller Differentialgleichungen (mit einer Anwendung auf die Theorie der Hohlraumstrahlung). Math. Ann. 71, 441–479 (German) (1912)MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Andreas Kriegl
    • 1
  • Peter W. Michor
    • 1
  • Armin Rainer
    • 1
  1. 1.Fakultät für MathematikUniversität WienWienAustria

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