(Non-)weakly mixing operators and hypercyclicity sets
Annales de l'Institut Fourier, Volume 59 (2009) no. 1, p. 1-35

We study the frequency of hypercyclicity of hypercyclic, non–weakly mixing linear operators. In particular, we show that on the space 1 (), any sublinear frequency can be realized by a non–weakly mixing operator. A weaker but similar result is obtained for c 0 () or p (), 1<p<. Part of our results is related to some Sidon-type lacunarity properties for sequences of natural numbers.

On étudie la fréquence d’hypercyclicité des opérateurs hypercycliques non faiblement mélangeants. On montre en particulier qu’il est possible de construire sur l’espace 1 des opérateurs non faiblement mélangeants de fréquence d’hypercyclicité arbitrairement grande. On obtient un résultat analogue (mais plus faible) sur c 0 ou p , 1<p<. Certains de nos résultats font intervenir des propriétés de lacunarité de type “Sidon” pour les suites d’entiers.

DOI : https://doi.org/10.5802/aif.2425
Classification:  47A16,  37B99,  11B99
Keywords: Hypercyclic operators, weak mixing, Sidon sequences
@article{AIF_2009__59_1_1_0,
     author = {Bayart, Fr\'ed\'eric and Matheron, \'Etienne},
     title = {(Non-)weakly mixing operators and hypercyclicity sets},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {59},
     number = {1},
     year = {2009},
     pages = {1-35},
     doi = {10.5802/aif.2425},
     mrnumber = {2514860},
     zbl = {1178.47003},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2009__59_1_1_0}
}
Bayart, Frédéric; Matheron, Étienne. (Non-)weakly mixing operators and hypercyclicity sets. Annales de l'Institut Fourier, Volume 59 (2009) no. 1, pp. 1-35. doi : 10.5802/aif.2425. http://www.numdam.org/item/AIF_2009__59_1_1_0/

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