Q-functions of Hermitian contractions of Krein-Ovcharenko type

YM Arlinskii*, Seppo Hassi, HSV de Snoo

*Corresponding author for this work

    Research output: Contribution to journalArticleAcademicpeer-review

    9 Citations (Scopus)

    Abstract

    In this paper operator-valued Q-functions of Krein-Ovcharenko type are introduced. Such functions arise from the extension theory of Hermitian contractive operators A in a Hilbert space h. The definition is related to the investigations of M.G. Krein and I.E. Ovcharenko of the so-called Q(mu) and Q(M)-functions. It turns out that their characterizations of such functions hold true only in the matrix valued case. The present paper extends the corresponding properties for wider classes of selfadjoint contractive extensions of A. For this purpose some peculiar but fundamental properties on the behaviour of operator ranges of positive operators will be used. Also proper characterizations for Q(mu)- and Q(M)-functions in the general operator-valued case are given. Shorted operators and parallel sums of positive operators will be needed to give a geometric understanding of the function-theoretic properties of the corresponding Q-functions.

    Original languageEnglish
    Pages (from-to)153-189
    Number of pages37
    JournalIntegral equations and operator theory
    Volume53
    Issue number2
    DOIs
    Publication statusPublished - Oct-2005

    Keywords

    • Hermitian contraction
    • selfadjoint extension
    • operator interval
    • extreme point
    • shorted operator
    • parallel sum
    • Q-function
    • SHORTED OPERATORS
    • PARALLEL ADDITION
    • EXTENSIONS
    • SPACE

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