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Elliptical Range Theorems for Generalized Numerical Ranges of Quadratic Operators
Li, Chi-Kwong Poon, Yiu-Tung Sze, Nung-Sing
Li, Chi-Kwong
Poon, Yiu-Tung
Sze, Nung-Sing
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.
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2011-01-01
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Mathematics
DOI
10.1216/RMJ-2011-41-3-813