Ratio Numerical Ranges of Operators

Abstract

Geometric properties of ratio numerical ranges of two Hilbert space operators are studied. Characterizations in terms of algebraic properties of operators are given for connectedness of ratio numerical ranges, and for the situations when the ratio numerical ranges are contained in a circle or in a line. Under a hypothesis of sectoriality (in a weak sense) simple connectedness of ratio numerical ranges is proved, and their boundedness property characterized.Mathematics Subject Classification (2010). Primary 47A12.