On Numerical Ranges of Rank-Two Operators

Leiba Rodman; Ilya M. Spitkovsky

doi:10.1007/s00020-013-2092-y

On Numerical Ranges of Rank-Two Operators

Leiba Rodman, Ilya M. Spitkovsky

Mathematics

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

Abstract

Possible shapes of numerical ranges of rank-two operators are studied. In particular it is proved that for 4-by-4 unitarily irreducible matrices with an eigenvalue of geometric multiplicity two, the numerical ranges have at most one flat portion on the boundary and there are no multiply generated round boundary points.

Original language	English (US)
Pages (from-to)	441-448
Number of pages	8
Journal	Integral Equations and Operator Theory
Volume	77
Issue number	3
DOIs	https://doi.org/10.1007/s00020-013-2092-y
State	Published - Nov 2013

Keywords

Numerical range
flat portion
multiply generated boundary points
rank-two operators

ASJC Scopus subject areas

Analysis
Algebra and Number Theory

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10.1007/s00020-013-2092-y

Cite this

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abstract = "Possible shapes of numerical ranges of rank-two operators are studied. In particular it is proved that for 4-by-4 unitarily irreducible matrices with an eigenvalue of geometric multiplicity two, the numerical ranges have at most one flat portion on the boundary and there are no multiply generated round boundary points.",

keywords = "Numerical range, flat portion, multiply generated boundary points, rank-two operators",

author = "Leiba Rodman and Spitkovsky, {Ilya M.}",

note = "Funding Information: I. M. Spitkovsky was partially supported by the William & Mary summer research grant and by the Plumeri award for faculty excellence.",

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N2 - Possible shapes of numerical ranges of rank-two operators are studied. In particular it is proved that for 4-by-4 unitarily irreducible matrices with an eigenvalue of geometric multiplicity two, the numerical ranges have at most one flat portion on the boundary and there are no multiply generated round boundary points.

AB - Possible shapes of numerical ranges of rank-two operators are studied. In particular it is proved that for 4-by-4 unitarily irreducible matrices with an eigenvalue of geometric multiplicity two, the numerical ranges have at most one flat portion on the boundary and there are no multiply generated round boundary points.

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KW - flat portion

KW - multiply generated boundary points

KW - rank-two operators

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ER -

On Numerical Ranges of Rank-Two Operators

Abstract

Keywords

ASJC Scopus subject areas

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