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

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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

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Keywords

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

ASJC Scopus subject areas

  • Analysis
  • Theoretical Computer Science
  • Mathematics(all)

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