A Birkhoff's transitivity type theorem for non-separable complete metric spaces with applications to Linear Dynamics

Details A Birkhoff's transitivity type theorem for non-separable complete metric spaces with applications to Linear Dynamics A Birkhoff's transitivity type theorem for non-separable complete metric spaces with applications to Linear Dynamics

2011-05-12

arxiv.org/abs/1105.2429v1

Mathematics

Functional Analysis

11 pages

Scientific paper

In this note we prove a Birkhoff's transitivity type theorem for non-separable complete metric spaces and we give some applications for dynamics of bounded linear operators on $F$-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 Ansari and Le\'{o}n-M\"{u}ller for hypercyclic operators.

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