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Extremal extensions for the sum of nonnegative selfadjoint relations |
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| Authors: | Seppo Hassi Adrian Sandovici Henk de Snoo Henrik Winkler |
| Affiliation: | Department of Mathematics and Statistics, University of Vaasa, P.O. Box 700, 65101 Vaasa, Finland ; Colegiul National ``Petru Rares', 610101, Str. Stefan cel Mare, Nr. 4, Piatra Neamt, Romania ; Department of Mathematics and Computing Science, University of Groningen, P.O. Box 800, 9700 AV Groningen, Nederland ; Institut für Mathematik, MA 6-4, Technische Universität Berlin, Strasse des 17. Juni 136, 10623 Berlin, Deutschland |
| 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  . |
| Keywords: | Nonnegative selfadjoint relation Friedrichs extension Kreu{i}n-von Neumann extension extremal extension form sum extension |
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