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On singular critical points of positive operators in Krein spaces


Authors: Branko Curgus, Aurelian Gheondea and Heinz Langer
Journal: Proc. Amer. Math. Soc. 128 (2000), 2621-2626
MSC (2000): Primary 47B50, 46C50
DOI: https://doi.org/10.1090/S0002-9939-00-05442-3
Published electronically: February 29, 2000
MathSciNet review: 1690979
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Abstract:

We give an example of a positive operator $B$ in a Krein space with the following properties: the nonzero spectrum of $B$ consists of isolated simple eigenvalues, the norms of the orthogonal spectral projections in the Krein space onto the eigenspaces of $B$ are uniformly bounded and the point $\infty$ is a singular critical point of $B.$


References [Enhancements On Off] (What's this?)

  • 1. T. Ya. Azizov, I. S. Iokhvidov, Linear operators in spaces with an indefinite metric. John Wiley & Sons, New York, 1989.MR 90j:47042
  • 2. B. Curgus, B. Najman, Quasi-uniformly positive operators in Krein spaces. Operator Theory and Boundary Eigenvalue Problems (Vienna, 1993), pp. 90-99, Oper. Theory: Adv. Appl., 80, Birkhäuser, Basel, 1995.MR 96j:47028
  • 3. P. Jonas, Über die Erhaltung der Stabilität $J$-positiver Operatoren bei $J$-positiven und $J$-negativen Störungen. Math. Nachr. 65 (1975), 211-218.MR 53:3786
  • 4. H. Langer, On maximal dual pairs of invariant subspaces of $J$-selfadjoint operators. Matem. Zametki 7 (1970), 443-447 (Russian).MR 42:3604
  • 5. H. Langer, Spectral functions of definitizable operators in Krein spaces. Functional Analysis, Proceedings, Dubrovnik 1981. Lecture Notes in Mathematics 948, Springer-Verlag, Berlin, 1982, 1-46.MR 84g:47034

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Additional Information

Branko Curgus
Affiliation: Department of Mathematics, Western Washington University, Bellingham, Washington 98225
Email: curgus@cc.wwu.edu

Aurelian Gheondea
Affiliation: Institutul de Matematică al Academiei Române, C.P. 1-764, 70700 Bucureşti, România
Email: gheondea@imar.ro

Heinz Langer
Affiliation: Institute for Analysis, Vienna Technical University, Wiedner Hauptstrasse 8-10, A-1040 Vienna, Austria
Email: hlanger@email.tuwien.ac.at

DOI: https://doi.org/10.1090/S0002-9939-00-05442-3
Keywords: Krein space, definitizable operator, critical point
Received by editor(s): October 15, 1998
Published electronically: February 29, 2000
Additional Notes: The third author was supported by Fonds zur Förderung der wissenschaftlichen Forschung of Austria, Project P 12176 MAT
Communicated by: David R. Larson
Article copyright: © Copyright 2000 American Mathematical Society

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