A characterization of semibounded selfadjoint operators
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- by Seppo Hassi, Michael Kaltenbäck and Henk de Snoo PDF
- Proc. Amer. Math. Soc. 125 (1997), 2681-2692 Request permission
Abstract:
For a class of closed symmetric operators $S$ with defect numbers $(1,1)$ it is possible to define a generalization of the Friedrichs extension, which coincides with the usual Friedrichs extension when $S$ is semibounded. In this paper we provide an operator-theoretic interpretation of this class of symmetric operators. Moreover, we prove that a selfadjoint operator $A$ is semibounded if and only if each one-dimensional restriction of $A$ has a generalized Friedrichs extension.References
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Additional Information
- Seppo Hassi
- Affiliation: Department of Statistics University of Helsinki PL 54, 00014 Helsinki Finland
- Email: hassi@cc.helsinki.fi
- Michael Kaltenbäck
- Affiliation: Institut für Analysis, Technische Mathematik und Versicherungsmathematik Technische Universität Wien Wiedner Hauptstrasse 8-10/114 A-1040 Wien Österreich
- Email: mbaeck@geometrie.tuwien.ac.at
- Henk de Snoo
- Affiliation: Department of Mathematics University of Groningen Postbus 800, 9700 AV Groningen Nederland
- Email: desnoo@math.rug.nl
- Received by editor(s): April 22, 1996
- Additional Notes: The second author was supported by “Fonds zur Förderung der wissenschaftlichen Forschung” of Austria, Project P 09832-MAT
- Communicated by: Palle E. T. Jorgensen
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 2681-2692
- MSC (1991): Primary 47B15, 47B25
- DOI: https://doi.org/10.1090/S0002-9939-97-03960-9
- MathSciNet review: 1403132