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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On singular critical points of positive operators in Krein spaces
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by Branko Ćurgus, Aurelian Gheondea and Heinz Langer PDF
Proc. Amer. Math. Soc. 128 (2000), 2621-2626 Request permission

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
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  • Branko Ćurgus and Branko Najman, Quasi-uniformly positive operators in Kreĭn space, Operator theory and boundary eigenvalue problems (Vienna, 1993) Oper. Theory Adv. Appl., vol. 80, Birkhäuser, Basel, 1995, pp. 90–99. MR 1362103
  • Peter Jonas, Über die Erhaltung der Stabilität $J$-positiver Operatoren bei $J$-positiven und $J$-negativen Störungen, Math. Nachr. 65 (1975), 211–218. MR 399948, DOI 10.1002/mana.19750650119
  • G. Langer, Maximal dual pairs of invariant subspaces of $J$-self-adjoint operators, Mat. Zametki 7 (1970), 443–447 (Russian). MR 268707
  • Heinz Langer, Spectral functions of definitizable operators in Kreĭn spaces, Functional analysis (Dubrovnik, 1981) Lecture Notes in Math., vol. 948, Springer, Berlin-New York, 1982, pp. 1–46. MR 672791
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Additional Information
  • Branko Ćurgus
  • 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
  • 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
  • © Copyright 2000 American Mathematical Society
  • 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
  • MathSciNet review: 1690979