Elliptical range theorems for generalized numerical ranges of quadratic operators

Chi Kwong Li, Yiu Tung Poon, Nung Sing Sze

Research output: Journal article publicationJournal articleAcademic researchpeer-review

11 Citations (Scopus)


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 languageEnglish
Pages (from-to)813-832
Number of pages20
JournalRocky Mountain Journal of Mathematics
Issue number3
Publication statusPublished - 8 Sept 2011


  • Davis-Wielandt shells
  • Elliptical ranges
  • Generalized numerical ranges
  • Quadratic operators

ASJC Scopus subject areas

  • Mathematics(all)


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