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

  • Type:

    Article

  • Date:

    24 February 2018

  • Publication Status:

    Published

  • Publisher

    Birkhauser Verlag Basel

  • DOI:

    10.1007/s11117-018-0566-5

  • Cross Ref:

    566

  • ISSN:

    1385-1292

  • Funders:

    Historic Funder (pre-Worktribe)

Citation

Guiver, C. (2018). On the strict monotonicity of spectral radii for classes of bounded positive linear operators. Positivity, 22, 1173-1190. https://doi.org/10.1007/s11117-018-0566-5

Authors

Keywords

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

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