A probabilistic version of the Frequent Hypercyclicity Criterion
Volume 176 / 2006
Studia Mathematica 176 (2006), 279-290
MSC: 47A16, 47A35, 46B09.
DOI: 10.4064/sm176-3-5
Abstract
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 $T^{n}x$ belongs to $U$, has positive lower density. This gives a connection between two different methods for obtaining the frequent hypercyclicity of operators.
