Mathematics – Functional Analysis
Scientific paper
2011-05-12
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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