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Extremal extensions for the sum of nonnegative selfadjoint relations
Author(s):
Seppo
Hassi;
Adrian
Sandovici;
Henk
de Snoo;
Henrik
Winkler
Journal:
Proc. Amer. Math. Soc.
135
(2007),
3193-3204.
MSC (2000):
Primary 47A57, 47B25;
Secondary 47A55, 47B65
Posted:
May 14, 2007
MathSciNet review:
2322750
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Abstract:
The sum  of two nonnegative selfadjoint relations (multi-valued operators)  and  is a nonnegative relation. The class of all extremal extensions of the sum  is characterized as products of relations via an auxiliary Hilbert space associated with  and  . The so-called form sum extension of  is a nonnegative selfadjoint extension, which is constructed via a closed quadratic form associated with  and  . Its connection to the class of extremal extensions is investigated and a criterion for its extremality is established, involving a nontrivial dependence on  and  .
References:
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- 1.
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- 2.
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- 4.
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- 7.
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- 9.
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Additional Information:
Seppo
Hassi
Affiliation:
Department of Mathematics and Statistics, University of Vaasa, P.O. Box 700, 65101 Vaasa, Finland
Email:
sha@uwasa.fi
Adrian
Sandovici
Affiliation:
Colegiul National ``Petru Rares'', 610101, Str. Stefan cel Mare, Nr. 4, Piatra Neamt, Romania
Email:
adrian.sandovici@yahoo.com
Henk
de Snoo
Affiliation:
Department of Mathematics and Computing Science, University of Groningen, P.O. Box 800, 9700 AV Groningen, Nederland
Email:
desnoo@math.rug.nl
Henrik
Winkler
Affiliation:
Institut für Mathematik, MA 6-4, Technische Universität Berlin, Strasse des 17. Juni 136, 10623 Berlin, Deutschland
Email:
winkler@math.tu-berlin.de
DOI:
10.1090/S0002-9939-07-08827-2
PII:
S 0002-9939(07)08827-2
Keywords:
Nonnegative selfadjoint relation,
Friedrichs extension,
Kre\u{\i}n-von Neumann extension,
extremal extension,
form sum extension
Received by editor(s):
March 27, 2006
Received by editor(s) in revised form:
June 15, 2006
Posted:
May 14, 2007
Additional Notes:
The fourth author was supported by the ``Fond zur Förderung der wissenschaftlichen Forschung'' (FWF, Austria), grant number P15540-N05.
Communicated by:
Joseph A. Ball
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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