On the boundary of rank-k numerical ranges

Abstract

Using the properties of the polynomial , Cheung and Li provided an alternative proof of Wu’s result on the circular symmetry of the classical numerical range. In this article, we further extend the idea and generalize Wu’s result to higher rank numerical ranges.

Keywords:

• rank-k numerical range
• unit disk

AMS Subject Classification:

• 15A60

Acknowledgments

We wish to thank Professor Chi-Kwong Li and the referee for their valuable comments. Many thanks to the referee for informing us of the construction of numerical ranges using critical curves and inspiring us to add Corollary 3.2.