### 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) |
---|---|

Pages (from-to) | 29-33 |

Number of pages | 5 |

Journal | Linear and Multilinear Algebra |

Volume | 47 |

Issue number | 1 |

State | Published - Dec 1 2000 |

### Fingerprint

### 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.

Research output: Contribution to journal › Article

*Linear and Multilinear Algebra*, vol. 47, no. 1, pp. 29-33.

}

TY - JOUR

T1 - On the non-round points of the boundary of the numerical range

AU - Spitkovsky, Ilya

PY - 2000/12/1

Y1 - 2000/12/1

N2 - 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.

AB - 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.

KW - Essential spectrum

KW - Numerical range

KW - Spectrum

UR - http://www.scopus.com/inward/record.url?scp=26444571462&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=26444571462&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:26444571462

VL - 47

SP - 29

EP - 33

JO - Linear and Multilinear Algebra

JF - Linear and Multilinear Algebra

SN - 0308-1087

IS - 1

ER -