Tarcsay, Zsigmond and Sebestyén, Zoltán (2023) Reduction of positive self-adjoint extensions. OPUSCULA MATHEMATICA. ISSN 1232-9274 (In Press)
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Abstract
We revise Krein’s extension theory of semi-bounded Hermitian operators by reducing the problem to finding all positive and contractive extensions of the ‘resolvent operator’ of T. Our treatment is somewhat simpler and more natural than Krein’s original method which was based on the Krein transform. Apart from being positive and symmetric, we do not impose any further constraints on the operator T: neither its closedness nor the density of its domain is assumed. Moreover, our arguments remain valid in both real or complex Hilbert spaces.
| Item Type: | Article |
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| Uncontrolled Keywords: | Positive selfadjoint contractive extension, nonnegative selfadjoint extension, Friedrichs and Krein-von Neumann extension |
| Subjects: | Q Science / természettudomány > QA Mathematics / matematika > QA74 Analysis / analízis |
| Depositing User: | Zsigmond Tarcsay |
| Date Deposited: | 27 Sep 2023 11:00 |
| Last Modified: | 27 Sep 2023 11:00 |
| URI: | http://real.mtak.hu/id/eprint/175242 |
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