(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

Abstract

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

How to cite

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Bayart, 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&lt;p&lt;\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&lt;p&lt;\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 -

References

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