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

Sahiba Arora; Jochen Glück

doi:10.5802/crmath.323

Analyse fonctionnelle, Théorie des opérateurs

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

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

Comptes Rendus. Mathématique, Volume 360 (2022), pp. 771-775.

Résumé

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.

Reçu le : 2021-12-15
Accepté le : 2022-01-04
Publié le : 2022-06-30

DOI : 10.5802/crmath.323

Classification : 47D06, 47B65, 47A10

Affiliations des auteurs :

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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     author = {Sahiba Arora and Jochen Gl\"uck},
     title = {Stability of (eventually) positive semigroups on spaces of continuous functions},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {771--775},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {360},
     year = {2022},
     doi = {10.5802/crmath.323},
     language = {en},
}

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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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