Ratio Numerical Ranges of Operators

Leiba Rodman, Ilya Spitkovsky

    Research output: Contribution to journalArticle

    Abstract

    Geometric properties of ratio numerical ranges of two Hilbert space operators are studied. Characterizations in terms of algebraic properties of operators are given for connectedness of ratio numerical ranges, and for the situations when the ratio numerical ranges are contained in a circle or in a line. Under a hypothesis of sectoriality (in a weak sense) simple connectedness of ratio numerical ranges is proved, and their boundedness property characterized.

    Original languageEnglish (US)
    Pages (from-to)245-257
    Number of pages13
    JournalIntegral Equations and Operator Theory
    Volume71
    Issue number2
    DOIs
    StatePublished - Oct 1 2011

    Fingerprint

    Numerical Range
    Connectedness
    Operator
    Boundedness
    Circle
    Hilbert space
    Line

    Keywords

    • Generalized numerical range
    • Hilbert space operators

    ASJC Scopus subject areas

    • Analysis
    • Algebra and Number Theory

    Cite this

    Ratio Numerical Ranges of Operators. / Rodman, Leiba; Spitkovsky, Ilya.

    In: Integral Equations and Operator Theory, Vol. 71, No. 2, 01.10.2011, p. 245-257.

    Research output: Contribution to journalArticle

    Rodman, Leiba ; Spitkovsky, Ilya. / Ratio Numerical Ranges of Operators. In: Integral Equations and Operator Theory. 2011 ; Vol. 71, No. 2. pp. 245-257.
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