Numerical ranges of the product of operators

Abstract

Abstract. 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.Mathematics subject classification (2010): 15A60, 47A12.

The numerical range of matrix products

“…What can be said about the numerical range W (A 1 A 2 ) of the product matrix A 1 A 2 ? There is some literature on this topic [1,3,4,6,9].…”