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

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

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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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