Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
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
Full-text PDF Free Access

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 $B.$

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

  • 1. 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 (90j:47042)
  • 2. 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 (96j:47028)
  • 3. Peter Jonas, Über die Erhaltung der Stabilität 𝐽-positiver Operatoren bei 𝐽-positiven und 𝐽-negativen Störungen, Math. Nachr. 65 (1975), 211–218. MR 0399948 (53 #3786)
  • 4. G. Langer, Maximal dual pairs of invariant subspaces of 𝐽-self-adjoint operators, Mat. Zametki 7 (1970), 443–447 (Russian). MR 0268707 (42 #3604)
  • 5. 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 (84g:47034)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 47B50, 46C50

Retrieve articles in all journals with MSC (2000): 47B50, 46C50

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

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

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia