Comptes Rendus
Analyse fonctionnelle, Théorie des opérateurs
Stability of (eventually) positive semigroups on spaces of continuous functions
Sahiba Arora1 ; Jochen Glück2
1 Technische Universität Dresden, Institut für Analysis, Fakultät für Mathematik, 01062 Dresden, Germany
2 Universität Passau, Fakultät für Informatik und Mathematik, 94032 Passau, Germany
Comptes Rendus. Mathématique, Volume 360 (2022), pp. 771-775.

We present a new and very short proof of the fact that, for positive C0-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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.5802/crmath.323
Classification : 47D06, 47B65, 47A10

Sahiba Arora 1 ; Jochen Glück 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
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Sahiba Arora; Jochen Glück. Stability of (eventually) positive semigroups on spaces of continuous functions. Comptes Rendus. Mathématique, Volume 360 (2022), pp. 771-775. doi : 10.5802/crmath.323. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.323/

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