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

 

Characterizations of positive selfadjoint extensions


Authors: Zoltán Sebestyén and Jan Stochel
Journal: Proc. Amer. Math. Soc. 135 (2007), 1389-1397
MSC (2000): Primary 47A20, 47B25; Secondary 47A63
Published electronically: October 27, 2006
MathSciNet review: 2276647
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Abstract: The set of all positive selfadjoint extensions of a positive operator $ T$ (which is not assumed to be densely defined) is described with the help of the partial order which is relevant to the theory of quadratic forms. This enables us to improve and extend a result of M. G. Krein to the case of not necessarily densely defined operators $ T$.


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Additional Information

Zoltán Sebestyén
Affiliation: Department of Applied Analysis, Eötvös L. University, Pázmány Péter sétány 1/c., Budapest H-1117, Hungary
Email: sebesty@cs.elte.hu

Jan Stochel
Affiliation: Instytut Matematyki, Uniwersytet Jagielloński, ul. Reymonta 4, PL-30059 Kraków, Poland
Email: stochel@im.uj.edu.pl

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08590-X
PII: S 0002-9939(06)08590-X
Keywords: Positive operator, selfadjoint operator, positive selfadjoint extension, Krein-von Neumann extension, Friedrichs extension
Received by editor(s): June 30, 2005
Received by editor(s) in revised form: November 29, 2005
Published electronically: October 27, 2006
Additional Notes: The research of the second author was supported by KBN grant 2 P03A 037 024
Dedicated: Dedicated to Henk de Snoo on the occasion of his sixtieth birthday.
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.