On the Bonsall cone spectral radius and the approximate point spectrum
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.
Keywords
Cite
@article{arxiv.1612.01755,
title = {On the Bonsall cone spectral radius and the approximate point spectrum},
author = {Vladimir Müller and Aljoša Peperko},
journal= {arXiv preprint arXiv:1612.01755},
year = {2016}
}