On the definition of the cone spectral radius

Gripenberg, Gustaf

doi:10.1090/S0002-9939-2014-12375-6

On the definition of the cone spectral radius
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by Gustaf Gripenberg PDF

Proc. Amer. Math. Soc. 143 (2015), 1617-1625 Request permission

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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