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Bounded Normal Operators in Pontryagin Spaces

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Operator Theory in Krein Spaces and Nonlinear Eigenvalue Problems

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 162))

Abstract

We establish some spectral properties of normal operators in a Pontryagin space Πκ. If κ = 1 a classification of the normal operators is given according to the structure of the eigenspaces of N and N+ which contain a non-positive eigenelement.

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References

  1. Azizov, Tomas Ya.; Iokhvidov, Iosif S.: Linear Operators in Spaces with an Indefinite Metric. John Wiley and Sons, Chichester, 1989.

    Google Scholar 

  2. Azizov, Tomas Ya.; Jonas, Peter: On compact perturbations of normal operators in a Krein space. Ukrainskii Matem. Žurnal 42 (1990), 1299–1306.

    MathSciNet  Google Scholar 

  3. Azizov, Tomas Ya.; Strauss, Vladimir A.: Spectral decompositions for special classes of self-adjoint and normal operators on Krein spaces. Theta Series in Advanced Mathematics: Spectral Analysis and its Applications, 45–67, The Theta Foundation, Bucharest, 2003.

    Google Scholar 

  4. Bognár, Janos: Indefinite Inner Product Spaces. Springer, New York-Heidelberg, 1974.

    Google Scholar 

  5. Gohberg, Israel; Reichstein, Boris: On classification of normal matrices in an indefinite scalar product. Integral Equations Operator Theory 13 (1990), 364–394.

    MathSciNet  Google Scholar 

  6. Jonas, Peter; Langer, Heinz: A model for π1-selfadjoint operators in π1-spaces and a special linear pencil. Integral Equations Operator Theory 8 (1985), 13–35.

    Article  MathSciNet  Google Scholar 

  7. Krein, Mark G.; Langer, Heinz: On the spectral function of a self-adjoint operator in a space with indefinite metric. Dokl. Akad. Nauk SSSR 152 (1963) 39–42 (Russian).

    MathSciNet  Google Scholar 

  8. Langer, Heinz: Habilitationsschrift Technische Universität Dresden, 1965.

    Google Scholar 

  9. Langer, Heinz: Invariante Teilräume definisierbarer J-selbstadjungierter Operatoren. Ann. Acad. Sci. Fenn. Ser. A I No. 475, 1971.

    Google Scholar 

  10. Langer, Heinz: Spectral functions of definitizable operators in Krein spaces. Functional analysis (Dubrovnik, 1981), Lecture Notes in Math., 948, 1–46, Springer, Berlin-New York, 1982.

    Google Scholar 

  11. Mehl, Christian; Ran, Andre; Rodman, Leiba: Semidefinite invariant subspaces: degenerate inner products, Operator Theory: Advances and Applications, 149 (2004), 467–486.

    MathSciNet  Google Scholar 

  12. Naimark, Mark A.: On commuting unitary operators in spaces with indefinite metric. Acta Sci. Math. (Szeged) 24 (1963), 177–189.

    MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Institute of Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstrasse 8-10, A-1040, Vienna, Austria

    Heinz Langer

  2. Instytut Matematyki, Uniwersytet Jagielloński, ul. Reymonta 4, PL-30059, Kraków, Poland

    Franciszek Hugon Szafraniec

Authors
  1. Heinz Langer
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  2. Franciszek Hugon Szafraniec
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Editor information

Editors and Affiliations

  1. Institut für Mathematik, Technische Universität Berlin, D-10623, Berlin, Germany

    Karl-Heinz Förster  & Peter Jonas  & 

  2. Institut für Analysis und Scientific Computing, Technische Universität Wien, A-1040, Wien, Austria

    Heinz Langer

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© 2005 Birkhäuser Verlag Basel/Switzerland

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Langer, H., Szafraniec, F.H. (2005). Bounded Normal Operators in Pontryagin Spaces. In: Förster, KH., Jonas, P., Langer, H. (eds) Operator Theory in Krein Spaces and Nonlinear Eigenvalue Problems. Operator Theory: Advances and Applications, vol 162. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7453-5_13

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