On the strict monotonicity of spectral radii for classes of bounded positive linear operators

Research output: Contribution to journalArticle

Abstract

Strict monotonicity of the spectral radii of bounded, positive, ordered linear operators is investigated. It is well-known that under reasonable assumptions, the spectral radii of two ordered positive operators enjoy a non-strict inequality. It is also well-known that a “strict” inequality between operators does not imply strict monotonicity of the spectral radii in general—some additional structure is required. We present a number of sufficient conditions on both the cone and the operators for such a strict ordering to hold which generalise known results in the literature, and have utility in comparison arguments, ubiquitous in positive systems theory.
Original languageEnglish
Pages (from-to)1173–1190
Number of pages18
JournalPositivity
Volume22
Issue number4
Early online date24 Feb 2018
DOIs
Publication statusPublished - 1 Sep 2018

Fingerprint

Positive Linear Operators
System theory
Spectral Radius
Bounded Linear Operator
Monotonicity
Mathematical operators
Cones
Positive Systems
Positive Operator
Operator
Systems Theory
Linear Operator
Cone
Imply
Generalise
Sufficient Conditions
Class

Keywords

  • Comparison argument
  • Ordered Banach space
  • Positive linear operator
  • Spectral radius

ASJC Scopus subject areas

  • Analysis
  • Theoretical Computer Science
  • Mathematics(all)

Cite this

On the strict monotonicity of spectral radii for classes of bounded positive linear operators. / Guiver, Christopher.

In: Positivity, Vol. 22, No. 4, 01.09.2018, p. 1173–1190.

Research output: Contribution to journalArticle

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