Ratio Numerical Ranges of Operators

Leiba Rodman, Ilya M. Spitkovsky

Research output: Contribution to journalArticlepeer-review


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
Issue number2
StatePublished - Oct 2011


  • Generalized numerical range
  • Hilbert space operators

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory


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