Numerical ranges of Foguel operators

Hwa Long Gau, Kuo Zhong Wang, Pei Yuan Wu

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


We study properties of the numerical ranges of Foguel operators [Formula presetend], where S is the simple unilateral shift and T is some operator, both acting on ℓ2. Among other things, we show that (1) if T is nonzero compact, then the numerical radius w(FT) is strictly less than 1+(‖T‖/2), (2) if T is a diagonal unitary operator, then 5/2<w(FT)≤3/2, and (3) if T is a scalar operator aI, then the numerical range W(FT) is open and is not a circular disc unless a=0.

Original languageEnglish
Pages (from-to)766-784
Number of pages19
JournalLinear Algebra and Its Applications
StatePublished - 1 Feb 2021


  • Foguel operator
  • Foguel–Halmos operator
  • Numerical radius
  • Numerical range


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