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On lifting of operators to Hilbert spaces induced by positive selfadjoint operators |
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| Authors: | Petru Cojuhari |
| Institution: | a Department of Applied Mathematics, AGH University of Science and Technology, Al. Mickievicza 30, 30-059 Cracow, Poland b Department of Mathematics, Bilkent University, 06800 Bilkent, Ankara, Turkey c Institutul de Matematic? al Academiei Române, C.P. 1-764, 70700 Bucure?ti, Romania |
| Abstract: | We introduce the notion of induced Hilbert spaces for positive unbounded operators and show that the energy spaces associated to several classical boundary value problems for partial differential operators are relevant examples of this type. The main result is a generalization of the Krein-Reid lifting theorem to this unbounded case and we indicate how it provides estimates of the spectra of operators with respect to energy spaces. |
| Keywords: | Energy space Induced Hilbert space Lifting of operators Boundary value problems Spectrum |
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