Lower spectral radius and spectral mapping theorem for suprema preserving mappings

Vladimir Müller; Aljoša Peperko

doi:10.3934/dcds.2018179

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2018, Volume 38, Issue 8: 4117-4132. Doi: 10.3934/dcds.2018179

This issue Previous Article Automatic sequences as good weights for ergodic theorems Next Article Global regularity for the 2D micropolar equations with fractional dissipation

Lower spectral radius and spectral mapping theorem for suprema preserving mappings

Vladimir Müller^1, and
Aljoša Peperko^2,3, ,

1.
Institute of Mathematics, Czech Academy of Sciences, Žitna 25, 115 67 Prague, Czech Republic
2.
Faculty of Mechanical Engineering, University of Ljubljana, Aškerčeva 6, SI-1000 Ljubljana, Slovenia
3.
Institute of Mathematics, Physics and Mechanics, Jadranska 19, SI-1000 Ljubljana, Slovenia

* Corresponding author: Aljoša Peperko
* Corresponding author: Aljoša Peperko

Received: October 31, 2017

Published: May 2018

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

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