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2007-01-01 - Article/Dans un journal avec peer-review - Anglais - 12 page(s)

Bernal-González L., Grosse-Erdmann Karl , "Existence and non-existence of hypercyclic semigroups" in Proceedings of the American Mathematical Society, 135, 3, 755-766

  • Edition : American Mathematical Society
  • Codes CREF : Mathématiques (DI1100), Systèmes chaotiques (DI1217)
  • Unités de recherche UMONS : Probabilité et statistique (S844)
  • Instituts UMONS : Institut de Recherche sur les Systèmes Complexes (Complexys)
Texte intégral :

Abstract(s) :

(Anglais) In these notes we provide a new proof of the existence of a hypercyclic uniformly continuous semigroup of operators on any separable infinite-dimensional Banach space that is very different from--and considerably shorter than--the one recently given by Bermúdez, Bonilla and Martinón. We also show the existence of a strongly dense family of topologically mixing operators on every separable infinite-dimensional Fréchet space. This complements recent results due to Bès and Chan. Moreover, we discuss the Hypercyclicity Criterion for semigroups and we give an example of a separable infinite-dimensional locally convex space which supports no supercyclic strongly continuous semigroup of operators

Notes :
  • (Anglais) ISSN 1088-6826(e
Identifiants :
  • ISSN : 0002-9939