A general factorization approach to the extension theory of nonnegative operators and relations

Seppo Hassi*, Adrian Sandovici, Henk De Snoo, Henrik Winkler

*Corresponding author for this work

    Research output: Contribution to journalArticleAcademicpeer-review

    36 Citations (Scopus)
    14 Downloads (Pure)

    Abstract

    The Krein-von Neumann and the Friedrichs extensions of a nonnegative linear operator or relation (i.e., a multivalued operator) are characterized in terms of factorizations. These factorizations lead to a novel approach to the transversality and equality of the Krein-von Neumann and the Friedrichs extensions and to the notion of positive closability (the Krein-von Neumann extension being an operator). Furthermore, all extremal extensions of the nonnegative operator or relation are characterized in terms of analogous factorizations. This approach for the general case of nonnegative linear relations in a Hilbert space extends the applicability of such factorizations. In fact, the extension theory of densely and nondensely defined nonnegative relations or operators fits in the same framework. In particular, all extremal extensions of a bounded nonnegative operator are characterized.

    Original languageEnglish
    Pages (from-to)351-386
    Number of pages36
    JournalJournal of operator theory
    Volume58
    Issue number2
    Publication statusPublished - 2007

    Keywords

    • nonnegative relation
    • Friedrichs extension
    • Krein-von Neumann extension
    • disjointness
    • transversality
    • positive closability
    • extremal extension
    • SELF-ADJOINT RELATIONS
    • EXTREMAL EXTENSIONS
    • PRODUCTS

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