English

Lower spectral radius and spectral mapping theorem for suprema preserving mappings

Spectral Theory 2017-12-04 v1

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.

Keywords

Cite

@article{arxiv.1712.00340,
  title  = {Lower spectral radius and spectral mapping theorem for suprema preserving mappings},
  author = {Vladimir Müller and Aljoša Peperko},
  journal= {arXiv preprint arXiv:1712.00340},
  year   = {2017}
}

Comments

arXiv admin note: text overlap with arXiv:1612.01755