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 | |
| Publication status | Published - 8 Sept 2011 |
Keywords
- Davis-Wielandt shells
- Elliptical ranges
- Generalized numerical ranges
- Quadratic operators
ASJC Scopus subject areas
- General Mathematics