A Birkhoff type transitivity theorem for non-separable completely metrizable spaces with applications to Linear Dynamics
Functional Analysis
2013-01-31 v2
Abstract
In this note we prove a Birkhoff type transitivity theorem for continuous maps acting on non-separable completely metrizable spaces and we give some applications for dynamics of bounded linear operators acting on complex Fr\'{e}chet spaces. Among them we show that any positive power and any unimodular multiple of a topologically transitive linear operator is topologically transitive, generalizing similar results of S.I. Ansari and F. Le\'{o}n-Saavedra V. M\"{u}ller for hypercyclic operators.
Cite
@article{arxiv.1105.2429,
title = {A Birkhoff type transitivity theorem for non-separable completely metrizable spaces with applications to Linear Dynamics},
author = {Antonios Manoussos},
journal= {arXiv preprint arXiv:1105.2429},
year = {2013}
}
Comments
Several changes concerning the presentation of the paper; title changed; 12 pages