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arXiv · 2108.05174

A note on the fixed space of positive contractions

Jochen Glück
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Abstract

We prove that, in a large class of Banach lattices, the fixed space of each commuting family of positive linear contractions is a lattice subspace. As consequences, new cyclicity results for the peripheral point spectra of positive operators and semigroups are derived; we also pose an open problem that naturally occurs in this context. Finally, a variety of counterexamples is presented to point out some limits of our results.

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Jochen Glück. 2021-08-11. A note on the fixed space of positive contractions. https://arxiv.org/abs/2108.05174

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