On the characterization of 2×2 ρ-contraction matrices

Kazuyoshi Okubo, Ilya Spitkovsky

Research output: Contribution to journalArticlepeer-review


We give an explicit description of all ρ-contractive (in Nagy-Foiaş sense) 2×2 matrices. This description leads to the formulas for ρ-numerical radii when the eigenvalues of such matrices either have equal absolute values or equal (modπ) arguments. We also discuss (natural) generalizations to the case of decomposable operators with at most two-dimensional blocks covering, in particular, the quadratic operators.

Original languageEnglish (US)
Pages (from-to)177-189
Number of pages13
JournalLinear Algebra and Its Applications
Issue number1-3
StatePublished - Mar 1 2001


  • 47A20
  • Decomposable operators
  • Primary 47A12
  • Secondary 15A60
  • ρ-Contractions
  • ρ-Numerical radii

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics


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