On the characterization of 2×2 ρ-contraction matrices

Kazuyoshi Okubo, Ilya Spitkovsky

Research output: Contribution to journalArticle

Abstract

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
Volume325
Issue number1-3
DOIs
StatePublished - Mar 1 2001

Fingerprint

Contraction
Numerical Radius
Decomposable
Operator
Absolute value
Covering
Eigenvalue
Generalization

Keywords

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

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis

Cite this

On the characterization of 2×2 ρ-contraction matrices. / Okubo, Kazuyoshi; Spitkovsky, Ilya.

In: Linear Algebra and Its Applications, Vol. 325, No. 1-3, 01.03.2001, p. 177-189.

Research output: Contribution to journalArticle

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