A QUANTITATIVE INTERPRETATION OF THE FREQUENT HYPERCYCLICITY CRITERION

Romuald Ernst (1) , A Mouze (2)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal
2 LPP - Laboratoire Paul Painlevé - UMR 8524

We give a quantitative interpretation of the Frequent Hypercyclicity Criterion. Actually we show that an operator which satisfies the Frequent Hypercyclicity Criterion is necessarily A-frequently hypercyclic, where A refers to some weighted densities sharper than the natural lower density. In that order, we exhibit different scales of weighted densities that are of interest to quantify the " frequency " measured by the Frequent Hypercyclicity Criterion. Moreover we construct an example of unilateral weighted shift which is frequently hypercyclic but not A-frequently hypercyclic on a particular scale.

Mots clés: Frequent Hypercyclicity Criterion; Weighted densities

Domaines: Analyse fonctionnelle [math.FA]

Romuald Ernst, A Mouze. A QUANTITATIVE INTERPRETATION OF THE FREQUENT HYPERCYCLICITY CRITERION. 2016. ⟨hal-01395490v1⟩