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On the definition of the cone spectral radius


Author: Gustaf Gripenberg
Journal: Proc. Amer. Math. Soc. 143 (2015), 1617-1625
MSC (2010): Primary 47H07
Published electronically: November 24, 2014
MathSciNet review: 3314074
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Abstract: For functions homogeneous of degree $ 1$ and mapping a cone into itself two reasonable definitions of the cone spectral radius have been given. Although they have been shown to be equal in many cases, this note gives an example showing that the two definitions may differ for continuous, homogeneous of degree one functions which are also order-preserving in the partial ordering induced by the cone.


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Gustaf Gripenberg
Affiliation: Department of Mathematics and Systems Analysis, Aalto University, Värmemansgränden 2, 02150 Espoo, Finland
Email: gustaf.gripenberg@aalto.fi

DOI: https://doi.org/10.1090/S0002-9939-2014-12375-6
Received by editor(s): May 24, 2013
Received by editor(s) in revised form: August 12, 2013
Published electronically: November 24, 2014
Communicated by: Thomas Schlumprecht
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.