Document Type
Article
Department/Program
Mathematics
Journal Title
Rocky Mountain Journal of Mathematics
Pub Date
2011
Volume
41
Issue
3
First Page
813
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.
Recommended Citation
Li, Chi-Kwong; Poon, Yiu-Tung; and Sze, Nung-Sing, Elliptical Range Theorems for Generalized Numerical Ranges of Quadratic Operators (2011). Rocky Mountain Journal of Mathematics, 41(3), 813-832.
10.1216/RMJ-2011-41-3-813
DOI
10.1216/RMJ-2011-41-3-813
