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ISSN 1088-6826(e) ISSN 0002-9939(p)

A characterization of semibounded selfadjoint operators

Author(s): Seppo Hassi; Michael Kaltenbäck; Henk de Snoo
Journal: Proc. Amer. Math. Soc. 125 (1997), 2681-2692.
MSC (1991): Primary 47B15, 47B25
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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:

[1]: E.A. Coddington and H.S.V. de Snoo, Positive selfadjoint extensions of positive symmetric subspaces, Math. Z., 159 (1978), 203-214. MR 58:17936
[2]: S. Hassi, M. Kaltenbäck, and H.S.V. de Snoo, Triplets of Hilbert spaces and Friedrichs extensions associated with the subclass ${\bf N}_1$ of Nevanlinna functions, J. Operator Theory, to appear.
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[4]: S. Hassi and H.S.V. de Snoo, One-dimensional graph perturbations of selfadjoint relations, Ann. Acad. Sci. Fenn., Series A.I. Math., 22 (1997), 123-164.
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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

DOI: 10.1090/S0002-9939-97-03960-9
PII: S 0002-9939(97)03960-9
Keywords: Symmetric operator, selfadjoint extension, Friedrichs extension, $Q$-function, Nevanlinna function
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 of article: Copyright 1997, American Mathematical Society

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