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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
Published electronically: February 29, 2000
MathSciNet review: 1690979
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Abstract | References | Similar Articles | Additional Information


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

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

Heinz Langer
Affiliation: Institute for Analysis, Vienna Technical University, Wiedner Hauptstrasse 8-10, A-1040 Vienna, Austria

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