A characterization of semibounded selfadjoint operators

Seppo Hassi, M Kaltenback, H DeSnoo

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    Abstract

    For a class of closed symmetric operators S with defect numbers (1, 1) it is possible to define a generalization of the Friedrichs extension, which coincides with the usual Friedrichs extension when S is semibounded. In this paper we provide an operator-theoretic interpretation of this class of symmetric operators. Moreover, we prove that a selfadjoint operator A is semibounded if and only if each one-dimensional restriction of A has a generalized Friedrichs extension.

    Original languageEnglish
    Pages (from-to)2681-2692
    Number of pages12
    JournalProceedings of the american mathematical society
    Volume125
    Issue number9
    Publication statusPublished - Sep-1997

    Keywords

    • Nevanlinna function
    • Q-function
    • Friedrichs extension
    • selfadjoint extension
    • symmetric operator

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