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On the Bonsall cone spectral radius and the approximate point spectrum

  • * Corresponding author: Aljoša Peperko

    * Corresponding author: Aljoša Peperko
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  • We study the Bonsall cone spectral radius and the approximate point spectrum of (in general non-linear) positively homogeneous, bounded and supremum preserving maps, defined on a max-cone in a given normed vector lattice. We prove that the Bonsall cone spectral radius of such maps is always included in its approximate point spectrum. Moreover, the approximate point spectrum always contains a (possibly trivial) interval. Our results apply to a large class of (nonlinear) max-type operators.

    We also generalize a known result that the spectral radius of a positive (linear) operator on a Banach lattice is contained in the approximate point spectrum. Under additional generalized compactness type assumptions our results imply Krein-Rutman type results.

    Mathematics Subject Classification: Primary: 47H07, 47J10, 47H10; Secondary: 47H08, 47B65, 47A10.


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