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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm176-3-5,
author = {Sophie Grivaux},
title = {A probabilistic version of the Frequent Hypercyclicity Criterion},
journal = {Studia Mathematica},
volume = {173},
year = {2006},
pages = {279-290},
zbl = {1111.47008},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm176-3-5}
}
Sophie Grivaux. A probabilistic version of the Frequent Hypercyclicity Criterion. Studia Mathematica, Tome 173 (2006) pp. 279-290. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm176-3-5/