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

Guiver, Chris

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.

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

• Journal Article Type: Article
• Acceptance Date: Feb 8, 2018
• Online Publication Date: Feb 24, 2018
• Publication Date: 2018-09
• Deposit Date: Jul 23, 2020
• Publicly Available Date: Jul 24, 2020
• Journal: Positivity
• Print ISSN: 1385-1292
• Electronic ISSN: 1572-9281
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 22
• Pages: 1173-1190
• DOI: https://doi.org/10.1007/s11117-018-0566-5
• Keywords: Comparison argument, Ordered Banach space, Positive linear operator, Spectral radius
• Public URL: http://researchrepository.napier.ac.uk/Output/2677283