Numerical range of the Foguel–Halmos operator

Hwa Long Gau, Kuo Zhong Wang, Pei Yuan Wu

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


We study properties of the numerical range of the Foguel–Halmos operator FT = [ S0∗ TS] on ℓ2 ⊕ ℓ2, where S is the simple unilateral shift and T = diag(a1, a2, . . .) with an = 1 if n = 3k for some k ≥ 1 and an = 0 otherwise. Among other things, we show that the numerical range W(FT ) is neither open nor closed, and give lower and upper bounds for the numerical radius w(FT ).

Original languageEnglish
Pages (from-to)267-292
Number of pages26
JournalStudia Mathematica
Issue number3
StatePublished - 2022


  • Foguel operator
  • Foguel–Halmos operator
  • numerical radius
  • numerical range


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