Hypercyclic operators, Gauss measures and Polish dynamical systems
Dynamical Systems
2020-10-07 v2 Functional Analysis
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.
Keywords
Cite
@article{arxiv.1211.0105,
title = {Hypercyclic operators, Gauss measures and Polish dynamical systems},
author = {Yiftach Dayan and Eli Glasner},
journal= {arXiv preprint arXiv:1211.0105},
year = {2020}
}
Comments
The new version corrects the statement and proof of Theorem 1.7