On partial isometries with circular numerical range

Abstract

In their LAMA 2016 paper Gau, Wang and Wu conjectured that a partial isometry A acting on ℂn cannot have a circular numerical range with a non-zero center, and proved this conjecture for n ≤ 4. We prove it for operators with rank A = n − 1 and any n.

Keywords

• numerical range
• partial isometry
• blaschke products
• poncelet’s porism
• elliptic functions
• interpolation
• 47a12
• 15a60
• 30j10
• 47b91
• 33e05
• 51m15