# A Birkhoff type transitivity theorem for non-separable completely metrizable spaces with applications to Linear Dynamics

Manoussos A (2013)

JOURNAL OF OPERATOR THEORY 70(1): 165-174.

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Manoussos, Antonios

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In this note we prove a Birkhoff type transitivity theorem for continuousmaps acting on non-separable completely metrizable spaces and we give someapplications for dynamics of bounded linear operators acting on complexFr\'{e}chet spaces. Among them we show that any positive power and anyunimodular multiple of a topologically transitive linear operator istopologically transitive, generalizing similar results of S.I. Ansari and F.Le\'{o}n-Saavedra V. M\"{u}ller for hypercyclic operators.

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Manoussos A. A Birkhoff type transitivity theorem for non-separable completely metrizable spaces with applications to Linear Dynamics.

*JOURNAL OF OPERATOR THEORY*. 2013;70(1):165-174.Manoussos, A. (2013). A Birkhoff type transitivity theorem for non-separable completely metrizable spaces with applications to Linear Dynamics.

*JOURNAL OF OPERATOR THEORY*,*70*(1), 165-174.Manoussos, A. (2013). A Birkhoff type transitivity theorem for non-separable completely metrizable spaces with applications to Linear Dynamics.

*JOURNAL OF OPERATOR THEORY*70, 165-174.Manoussos, A., 2013. A Birkhoff type transitivity theorem for non-separable completely metrizable spaces with applications to Linear Dynamics.

*JOURNAL OF OPERATOR THEORY*, 70(1), p 165-174.A. Manoussos, “A Birkhoff type transitivity theorem for non-separable completely metrizable spaces with applications to Linear Dynamics”,

*JOURNAL OF OPERATOR THEORY*, vol. 70, 2013, pp. 165-174.Manoussos, A.: A Birkhoff type transitivity theorem for non-separable completely metrizable spaces with applications to Linear Dynamics. JOURNAL OF OPERATOR THEORY. 70, 165-174 (2013).

Manoussos, Antonios. “A Birkhoff type transitivity theorem for non-separable completely metrizable spaces with applications to Linear Dynamics”.

*JOURNAL OF OPERATOR THEORY*70.1 (2013): 165-174.
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arXiv 1105.2429