On the characterization of 2×2 ρ-contraction matrices

Kazuyoshi Okubo; Ilya Spitkovsky

doi:10.1016/S0024-3795(00)00265-2

On the characterization of 2×2 ρ-contraction matrices

Kazuyoshi Okubo, Ilya Spitkovsky

Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English (US)
Pages (from-to)	177-189
Number of pages	13
Journal	Linear Algebra and Its Applications
Volume	325
Issue number	1-3
DOIs	https://doi.org/10.1016/S0024-3795(00)00265-2
State	Published - Mar 1 2001

Keywords

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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10.1016/S0024-3795(00)00265-2

Cite this

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title = "On the characterization of 2×2 ρ-contraction matrices",

abstract = "We give an explicit description of all ρ-contractive (in Nagy-Foia{\c s} 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.",

keywords = "47A20, Decomposable operators, Primary 47A12, Secondary 15A60, ρ-Contractions, ρ-Numerical radii",

author = "Kazuyoshi Okubo and Ilya Spitkovsky",

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AU - Spitkovsky, Ilya

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N2 - 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.

AB - 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.

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KW - Secondary 15A60

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KW - ρ-Numerical radii

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JO - Linear Algebra and Its Applications

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On the characterization of 2×2 ρ-contraction matrices

Abstract

Keywords

ASJC Scopus subject areas

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