Elliptical range theorems for generalized numerical ranges of quadratic operators
Chi-Kwong Li, Yiu‐Tung Poon, Nung-Sing Sze · Rocky Mountain Journal of Mathematics · 2011
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. AMS Subject Classification 47A12, 15A60 Keywords Quadratic operators, elliptical ranges, generalized numerical ranges, Davis-