### 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.

Original language | English (US) |
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Pages (from-to) | 245-257 |

Number of pages | 13 |

Journal | Integral Equations and Operator Theory |

Volume | 71 |

Issue number | 2 |

DOIs | |

State | Published - Oct 2011 |

### Keywords

- Generalized numerical range
- Hilbert space operators

### ASJC Scopus subject areas

- Analysis
- Algebra and Number Theory

## Fingerprint Dive into the research topics of 'Ratio Numerical Ranges of Operators'. Together they form a unique fingerprint.

## Cite this

Rodman, L., & Spitkovsky, I. M. (2011). Ratio Numerical Ranges of Operators.

*Integral Equations and Operator Theory*,*71*(2), 245-257. https://doi.org/10.1007/s00020-011-1898-8