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

Received:
Revised:
Accepted:
DOI: 10.5802/aif.2425
Classification: 47A16,  37B99,  11B99
Keywords: Hypercyclic operators, weak mixing, Sidon sequences
Bayart, Frédéric 1; Matheron, Étienne 2

1 Université Blaise Pascal Laboratoire de Mathématiques Campus universitaire des Cézeaux 63177 Aubières Cedex (France)
2 Université d’Artois Laboratoire de Mathématiques de Lens Rue Jean Souvraz S.P. 18 62307 Lens (France)
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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. https://aif.centre-mersenne.org/articles/10.5802/aif.2425/

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