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On the nonnegativity of operator products |
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| Authors: | Seppo Hassi Zoltán Sebestyén Henk de Snoo |
| Institution: | 23101. Department of Mathematics and Statistics, University of Vaasa, P.O. Box 700, 65101 Vaasa, Finland 23102. Department of Applied Analysis, E?tv?s Loránd University, Pázmány Péter sétány 1/C 1117 Budapest 23103. Department of Mathematics and Computing Science, University of Groningen, P.O. Box 800, 9700 av Groningen, Nederland |
| Abstract: | Summary A bounded, not necessarily everywhere defined, nonnegative operator A in a Hilbert space <InlineEquation ID=IE"1"><EquationSource Format="TEX"><!CDATA<InlineEquation ID=IE"2"><EquationSource Format="TEX"><!CDATA$]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>\mathfrak{H}$ is assumed to intertwine in a certain sense two bounded everywhere defined operators B and C. If the range of A is provided with a natural inner product then the operators B and C induce two new operators on the completion space. This construction is used to show the existence of selfadjoint and nonnegative extensions of B*A and C*A. |
| Keywords: | Friedrichs extension symmetric operator selfadjoint operator product of operators nonnegative operator Kre?n-von Neumann extension |
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