A probabilistic version of the Frequent Hypercyclicity Criterion

Sophie Grivaux. "A probabilistic version of the Frequent Hypercyclicity Criterion." Studia Mathematica 176.3 (2006): 279-290. <http://eudml.org/doc/284406>.

@article{SophieGrivaux2006,
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 Tⁿx belongs to U, has positive lower density. This gives a connection between two different methods for obtaining the frequent hypercyclicity of operators.},
author = {Sophie Grivaux},
journal = {Studia Mathematica},
keywords = {linear dynamical systems; frequently hypercyclic operators; frequent hypercyclicity criterion; Gaussian mesures; Gaussian sums of Banach spaces},
language = {eng},
number = {3},
pages = {279-290},
title = {A probabilistic version of the Frequent Hypercyclicity Criterion},
url = {http://eudml.org/doc/284406},
volume = {176},
year = {2006},
}

TY - JOUR
AU - Sophie Grivaux
TI - A probabilistic version of the Frequent Hypercyclicity Criterion
JO - Studia Mathematica
PY - 2006
VL - 176
IS - 3
SP - 279
EP - 290
AB - 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.
LA - eng
KW - linear dynamical systems; frequently hypercyclic operators; frequent hypercyclicity criterion; Gaussian mesures; Gaussian sums of Banach spaces
UR - http://eudml.org/doc/284406
ER -