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arXiv · 1211.0105

Hypercyclic operators, Gauss measures and Polish dynamical systems

Yiftach Dayan·Eli Glasner
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Abstract

In this work we consider hypercyclic operators as a special case of Polish dynamical systems. In the first section we analyze the construction of Bayart and Grivaux of a hypercyclic operator which preserves a Gaussian measure, and derive a description of the maximal spectral type of the Koopman operator associated to the corresponding measure preserving dynamical system. We then use this information to show the existence of a mildly but not strongly mixing hypercyclic operator on Hilbert space. In the last two sections we study hypercyclic and frequently hypecyclic operators which, as Polish dynamical systems are, M-systems, E-systems, and syndetically transitive systems.

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Yiftach Dayan, Eli Glasner. 2012-11-01. Hypercyclic operators, Gauss measures and Polish dynamical systems. https://arxiv.org/abs/1211.0105

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