### 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 language | English (US) |
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Pages (from-to) | 29-33 |

Number of pages | 5 |

Journal | Linear and Multilinear Algebra |

Volume | 47 |

Issue number | 1 |

Publication status | Published - Dec 1 2000 |

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### Keywords

- Essential spectrum
- Numerical range
- Spectrum

### ASJC Scopus subject areas

- Algebra and Number Theory