A probabilistic version of the Frequent Hypercyclicity Criterion

• Autorzy: Sophie Grivaux
• Języki publikacji: EN

Abstrakty

EN

For a bounded operator T on a separable infinite-dimensional Banach space X, we give a "random" criterion not involving ergodic theory which implies that T is frequently hypercyclic: there exists a vector x such that for every non-empty open subset U of X, the set of integers n such that Tⁿx belongs to U, has positive lower density. This gives a connection between two different methods for obtaining the frequent hypercyclicity of operators.

Kategorie tematyczne

• 47A35: Ergodic theory
• 47A16: Cyclic vectors, hypercyclic and chaotic operators
• 46B09: Probabilistic methods in Banach space theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2006
• Tom: 176
• Numer: 3
• Strony: 279-290

Daty

wydano

2006

Twórcy

autor

Sophie Grivaux

• Laboratoire Paul Painlevé, UMR 8524, Université des Sciences et Technologies de Lille, Bâtiment M2, Cité Scientifique, 59655 Villeneuve d'Ascq Cedex, France

Identyfikatory

DOI

10.4064/sm176-3-5