On the non-round points of the boundary of the numerical range

Ilya Spitkovsky

    Research output: Contribution to journalArticle

    Abstract

    Let A be a bounded linear operator acting on a Hilbert space. It is well known (Donoghue, 1957) that corner points of the numerical range W(A) are eigenvalues of A. Recently (1995), this result was generalized by Hübner who showed that points of infinite curvature on the boundary of W(A) lie in the spectrum of A. Hübner also conjectured that all such points are either corner points or lie in the essential spectrum of A. In this paper, we give a short proof of this conjecture.

    Original languageEnglish (US)
    Pages (from-to)29-33
    Number of pages5
    JournalLinear and Multilinear Algebra
    Volume47
    Issue number1
    StatePublished - Dec 1 2000

    Fingerprint

    Numerical Range
    Essential Spectrum
    Bounded Linear Operator
    Hilbert space
    Curvature
    Eigenvalue

    Keywords

    • Essential spectrum
    • Numerical range
    • Spectrum

    ASJC Scopus subject areas

    • Algebra and Number Theory

    Cite this

    On the non-round points of the boundary of the numerical range. / Spitkovsky, Ilya.

    In: Linear and Multilinear Algebra, Vol. 47, No. 1, 01.12.2000, p. 29-33.

    Research output: Contribution to journalArticle

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