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

Ilya M. Spitkovsky

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

Ilya M. Spitkovsky

Mathematics

Research output: Contribution to journal › Article › peer-review

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 - 2000

Keywords

Essential spectrum
Numerical range
Spectrum

ASJC Scopus subject areas

Algebra and Number Theory

Cite this

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title = "On the non-round points of the boundary of the numerical range",

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 H{\"u}bner who showed that points of infinite curvature on the boundary of W(A) lie in the spectrum of A. H{\"u}bner 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.",

keywords = "Essential spectrum, Numerical range, Spectrum",

author = "Spitkovsky, {Ilya M.}",

note = "Funding Information: *The results of this paper were discussed at the Fourth Workshop on Numerical Ranges and Numerical Radii held at Madison in 1998. h he author was supported in part by NSF Grant DMS #9800704. e-mail: ilya&math.wm.edu",

year = "2000",

language = "English (US)",

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N1 - Funding Information: *The results of this paper were discussed at the Fourth Workshop on Numerical Ranges and Numerical Radii held at Madison in 1998. h he author was supported in part by NSF Grant DMS #9800704. e-mail: ilya&math.wm.edu

PY - 2000

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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

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M3 - Article

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JO - Linear and Multilinear Algebra

JF - Linear and Multilinear Algebra

IS - 1

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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