Elliptical range theorems for generalized numerical ranges of quadratic operators

Chi Kwong Li; Yiu Tung Poon; Nung Sing Sze

doi:10.1216/RMJ-2011-41-3-813

Elliptical range theorems for generalized numerical ranges of quadratic operators

Chi Kwong Li, Yiu Tung Poon, Nung Sing Sze

Research output: Journal article publication › Journal article › Academic research › peer-review

11 Citations (Scopus)

Abstract

The classical numerical range of a quadratic operator is an elliptical disk. This result is extended to different kinds of generalized numerical ranges. In particular, it is shown that for a given quadratic operator, the rank-k numerical range, the essential numerical range, and the q-numerical range are elliptical disks; the c-numerical range is a sum of elliptical disks, and the Davis-Wielandt shell is an ellipsoid with or without interior.

Original language	English
Pages (from-to)	813-832
Number of pages	20
Journal	Rocky Mountain Journal of Mathematics
Volume	41
Issue number	3
DOIs	https://doi.org/10.1216/RMJ-2011-41-3-813
Publication status	Published - 8 Sept 2011

Keywords

Davis-Wielandt shells
Elliptical ranges
Generalized numerical ranges
Quadratic operators

ASJC Scopus subject areas

Mathematics(all)

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10.1216/RMJ-2011-41-3-813

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Elliptical range theorems for generalized numerical ranges of quadratic operators

Abstract

Keywords

ASJC Scopus subject areas

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