# (Non-)weakly mixing operators and hypercyclicity sets

Frédéric Bayart^{[1]}; Étienne Matheron^{[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)

Annales de l’institut Fourier (2009)

- Volume: 59, Issue: 1, page 1-35
- ISSN: 0373-0956

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topBayart, Frédéric, and Matheron, Étienne. "(Non-)weakly mixing operators and hypercyclicity sets." Annales de l’institut Fourier 59.1 (2009): 1-35. <http://eudml.org/doc/10391>.

@article{Bayart2009,

abstract = {We study the frequency of hypercyclicity of hypercyclic, non–weakly mixing linear operators. In particular, we show that on the space $\ell ^1(\mathbb\{N\})$, any sublinear frequency can be realized by a non–weakly mixing operator. A weaker but similar result is obtained for $c_0(\mathbb\{N\})$ or $\ell ^p(\mathbb\{N\})$, $1<p<\infty $. Part of our results is related to some Sidon-type lacunarity properties for sequences of natural numbers.},

affiliation = {Université Blaise Pascal Laboratoire de Mathématiques Campus universitaire des Cézeaux 63177 Aubières Cedex (France); Université d’Artois Laboratoire de Mathématiques de Lens Rue Jean Souvraz S.P. 18 62307 Lens (France)},

author = {Bayart, Frédéric, Matheron, Étienne},

journal = {Annales de l’institut Fourier},

keywords = {Hypercyclic operators; weak mixing; Sidon sequences; hypercyclic operators},

language = {eng},

number = {1},

pages = {1-35},

publisher = {Association des Annales de l’institut Fourier},

title = {(Non-)weakly mixing operators and hypercyclicity sets},

url = {http://eudml.org/doc/10391},

volume = {59},

year = {2009},

}

TY - JOUR

AU - Bayart, Frédéric

AU - Matheron, Étienne

TI - (Non-)weakly mixing operators and hypercyclicity sets

JO - Annales de l’institut Fourier

PY - 2009

PB - Association des Annales de l’institut Fourier

VL - 59

IS - 1

SP - 1

EP - 35

AB - We study the frequency of hypercyclicity of hypercyclic, non–weakly mixing linear operators. In particular, we show that on the space $\ell ^1(\mathbb{N})$, any sublinear frequency can be realized by a non–weakly mixing operator. A weaker but similar result is obtained for $c_0(\mathbb{N})$ or $\ell ^p(\mathbb{N})$, $1<p<\infty $. Part of our results is related to some Sidon-type lacunarity properties for sequences of natural numbers.

LA - eng

KW - Hypercyclic operators; weak mixing; Sidon sequences; hypercyclic operators

UR - http://eudml.org/doc/10391

ER -

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