On singular critical points of positive operators in Krein spaces
HTML articles powered by AMS MathViewer
- 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
- T. Ya. Azizov and I. S. Iokhvidov, Linear operators in spaces with an indefinite metric, Pure and Applied Mathematics (New York), John Wiley & Sons, Ltd., Chichester, 1989. Translated from the Russian by E. R. Dawson; A Wiley-Interscience Publication. MR 1033489
- 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
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