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Article Contents

# Lower spectral radius and spectral mapping theorem for suprema preserving mappings

• * Corresponding author: Aljoša Peperko
• 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.

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

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