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

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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
Issue number1
StatePublished - 2000


  • Essential spectrum
  • Numerical range
  • Spectrum

ASJC Scopus subject areas

  • Algebra and Number Theory


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