On the Bonsall cone spectral radius and the approximate point spectrum

Vladimir Müller; Aljoša Peperko

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arXiv · 1612.01755

On the Bonsall cone spectral radius and the approximate point spectrum

Vladimir Müller·Aljoša Peperko

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Abstract

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.

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BibTeX RIS

Vladimir Müller, Aljoša Peperko. 2016-12-06. On the Bonsall cone spectral radius and the approximate point spectrum. https://arxiv.org/abs/1612.01755

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