Ratio Numerical Ranges of Operators

Leiba Rodman, Ilya M. Spitkovsky

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)245-257
Number of pages13
JournalIntegral Equations and Operator Theory
Volume71
Issue number2
DOIs
StatePublished - Oct 2011

Keywords

  • Generalized numerical range
  • Hilbert space operators

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory

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