Analyse fonctionnelle, Théorie des opérateurs
Stability of (eventually) positive semigroups on spaces of continuous functions
Comptes Rendus. Mathématique, Tome 360 (2022) no. G7, pp. 771-775.

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.

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DOI : 10.5802/crmath.323
Classification : 47D06, 47B65, 47A10
Arora, Sahiba 1 ; Glück, Jochen 2

1 Technische Universität Dresden, Institut für Analysis, Fakultät für Mathematik, 01062 Dresden, Germany
2 Universität Passau, Fakultät für Informatik und Mathematik, 94032 Passau, Germany
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Arora, Sahiba; Glück, Jochen. Stability of (eventually) positive semigroups on spaces of continuous functions. Comptes Rendus. Mathématique, Tome 360 (2022) no. G7, pp. 771-775. doi : 10.5802/crmath.323. http://www.numdam.org./articles/10.5802/crmath.323/

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