Numerical ranges of the product of operators

Hongke Du, Chi Kwong Li, Kuo-Zhong Wang, Yueqing Wang*, Ning Zuo

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


We study containment regions of the numerical range of the product of operators A and B such that W(A) and W(B) are line segments. It is shown that the containment region is equal to the convex hull of elliptical disks determined by the spectrum of AB, and conditions on A and B for the set equality holding are obtained. The results cover the case when A and B are self-adjoint operators extending the previous results on the numerical range of the product of two orthogonal projections.

Original languageEnglish
Article number11-12
Pages (from-to)171-180
Number of pages10
JournalOperators and Matrices
Issue number1
StatePublished - 1 Mar 2017


  • Numerical range
  • Product of matrices and operators

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