On Numerical Ranges of Rank-Two Operators

Leiba Rodman, Ilya Spitkovsky

    Research output: Contribution to journalArticle

    Abstract

    Possible shapes of numerical ranges of rank-two operators are studied. In particular it is proved that for 4-by-4 unitarily irreducible matrices with an eigenvalue of geometric multiplicity two, the numerical ranges have at most one flat portion on the boundary and there are no multiply generated round boundary points.

    Original languageEnglish (US)
    Pages (from-to)441-448
    Number of pages8
    JournalIntegral Equations and Operator Theory
    Volume77
    Issue number3
    DOIs
    StatePublished - Nov 1 2013

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    Numerical Range
    Irreducible Matrix
    Operator
    Multiplicity
    Multiplication
    Eigenvalue

    Keywords

    • flat portion
    • multiply generated boundary points
    • Numerical range
    • rank-two operators

    ASJC Scopus subject areas

    • Analysis
    • Algebra and Number Theory

    Cite this

    On Numerical Ranges of Rank-Two Operators. / Rodman, Leiba; Spitkovsky, Ilya.

    In: Integral Equations and Operator Theory, Vol. 77, No. 3, 01.11.2013, p. 441-448.

    Research output: Contribution to journalArticle

    Rodman, Leiba ; Spitkovsky, Ilya. / On Numerical Ranges of Rank-Two Operators. In: Integral Equations and Operator Theory. 2013 ; Vol. 77, No. 3. pp. 441-448.
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