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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
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 $B.$


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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: http://dx.doi.org/10.1090/S0002-9939-00-05442-3
PII: S 0002-9939(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