Reduction of positive self-adjoint extensions

• Autorzy: Tarcsay Zsigmond , Sebestyén Zoltán

Identyfikatory

DOI

10.7494/OpMath.2024.44.3.425

• Języki publikacji: EN

Abstrakty

EN

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” (I + T)−1 of T. Our treatment is somewhat simpler and more natural than Krein’s original method which was based on the Krein transform (I−T)(I+T)−1. 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.

Słowa kluczowe

EN

positive selfadjoint contractive extension; nonnegative selfadjoint extension; Friedrichs and Krein-von Neumann extension

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2024
• Tom: Vol. 44, no. 3
• Strony: 425--438
• Opis fizyczny: Bibliogr. 29 poz.

Twórcy

autor

Tarcsay Zsigmond

• Corvinus University of Budapest, Department of Mathematics, IX. Fővám tér 13–15, Budapest H-1093, Hungary
• Eötvös Loránd University, Department of Applied Analysis and Computational Mathematics, Pázmány Péter sétány 1/c, Budapest H-1117, Hungary

• https://orcid.org/0000-0001-8102-5055

autor

Sebestyén Zoltán

• Eötvös Loránd University, Department of Applied Analysis and Computational Mathematics, Pázmány Péter sétány 1/c, Budapest H-1117, Hungary

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Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023)