### 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) |
---|---|

Pages (from-to) | 245-257 |

Number of pages | 13 |

Journal | Integral Equations and Operator Theory |

Volume | 71 |

Issue number | 2 |

DOIs | |

State | Published - Oct 1 2011 |

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### Keywords

- Generalized numerical range
- Hilbert space operators

### ASJC Scopus subject areas

- Analysis
- Algebra and Number Theory

### Cite this

*Integral Equations and Operator Theory*,

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

**Ratio Numerical Ranges of Operators.** / Rodman, Leiba; Spitkovsky, Ilya.

Research output: Contribution to journal › Article

*Integral Equations and Operator Theory*, vol. 71, no. 2, pp. 245-257. https://doi.org/10.1007/s00020-011-1898-8

}

TY - JOUR

T1 - Ratio Numerical Ranges of Operators

AU - Rodman, Leiba

AU - Spitkovsky, Ilya

PY - 2011/10/1

Y1 - 2011/10/1

N2 - 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.

AB - 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.

KW - Generalized numerical range

KW - Hilbert space operators

UR - http://www.scopus.com/inward/record.url?scp=80053271496&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80053271496&partnerID=8YFLogxK

U2 - 10.1007/s00020-011-1898-8

DO - 10.1007/s00020-011-1898-8

M3 - Article

VL - 71

SP - 245

EP - 257

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

SN - 0378-620X

IS - 2

ER -