Ratio Numerical Ranges of Operators

Leiba Rodman; Ilya M. Spitkovsky

doi:10.1007/s00020-011-1898-8

Ratio Numerical Ranges of Operators

Leiba Rodman, Ilya M. Spitkovsky

Mathematics

Research output: Contribution to journal › Article › peer-review

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	https://doi.org/10.1007/s00020-011-1898-8
State	Published - Oct 2011

Keywords

Generalized numerical range
Hilbert space operators

ASJC Scopus subject areas

Analysis
Algebra and Number Theory

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10.1007/s00020-011-1898-8

Cite this

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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.

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Ratio Numerical Ranges of Operators

Abstract

Keywords

ASJC Scopus subject areas

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