Lower spectral radius and spectral mapping theorem for suprema preserving mappings

Vladimir Müller; Aljoša Peperko

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arXiv · 1712.00340

Lower spectral radius and spectral mapping theorem for suprema preserving mappings

Vladimir Müller·Aljoša Peperko

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Abstract

We study Lipschitz, positively homogeneous and finite suprema preserving mappings defined on a max-cone of positive elements in a normed vector lattice. We prove that the lower spectral radius of such a mapping is always a minimum value of its approximate point spectrum. We apply this result to show that the spectral mapping theorem holds for the approximate point spectrum of such a mapping. By applying this spectral mapping theorem we obtain new inequalites for the Bonsall cone spectral radius of max type kernel operators.

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BibTeX RIS

Vladimir Müller, Aljoša Peperko. 2017-11-29. Lower spectral radius and spectral mapping theorem for suprema preserving mappings. https://arxiv.org/abs/1712.00340

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