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Eigenvectors of homogeneous order-bounded order-preserving maps

  • Author Bio: E-mail address: hthieme@asu.edu
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  • The existence of eigenvectors associated with the cone spectral radius is shown for homogenous, order-preserving, continuous maps that have compact and order-bounded powers (iterates). The order-boundedness makes it possible to show the existence of eigenvectors for perturbations of the maps using Hilbert's projective metric, while the power compactness or similar compactness properties together with a uniform continuity condition let the eigenvectors of the perturbations converge to an eigenvector of the original map.

    Mathematics Subject Classification: Primary:47H07, 47J10;Secondary:47N60.


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