Numerical ranges of the product of operators
Hong Du, Chi-Kwong Li, Kuo-Zhong Wang, Yueq ng Wang, Ning Zuo · Operators and Matrices · 2017
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.