Stability of (eventually) positive semigroups on spaces of continuous functions

Abstract

We present a new and very short proof of the fact that, for positive $C_0$-semigroups on spaces of continuous functions, the spectral and the growth bound coincide. Our argument, inspired by an idea of Vogt, makes the role of the underlying space completely transparent and also works if the space does not contain the constant functions - a situation in which all earlier proofs become technically quite involved. We also show how the argument can be adapted to yield the same result for semigroups that are only eventually positive rather than positive.

arXiv comment5 pages. This is version 2; minor changes compared to v1

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Cited by in corpus (2)

• Growth rate of eventually positive Kreiss bounded $C_0$-semigroups on $L^p$ and $\mathcal{C}(K)$
• Eventually positive semigroups: spectral and asymptotic analysis