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Studia Mathematica

2006 | 175 | 3 | 249-269

Somewhere dense Cesàro orbits and rotations of Cesàro hypercyclic operators

EN

Abstrakty

EN
Let T be a continuous linear operator acting on a Banach space X. We examine whether certain fundamental results for hypercyclic operators are still valid in the Cesàro hypercyclicity setting. In particular, in connection with the somewhere dense orbit theorem of Bourdon and Feldman, we show that if for some vector x ∈ X the set {Tx,T²/2 x,T³/3 x, ... } is somewhere dense then for every 0 < ε < 1 the set (0,ε){Tx,T²/2 x,T³/3 x,...} is dense in X. Inspired by a result of Feldman, we also prove that if the sequence ${n^{-1}Tⁿx}$ is d-dense then the operator T is Cesàro hypercyclic. Finally, following the work of León-Saavedra and Müller, we consider rotations of Cesàro hypercyclic operators and we establish that in certain cases, for any λ with |λ | = 1, T and λT share the same sets of Cesàro hypercyclic vectors.

249-269

wydano
2006

Twórcy

autor
• Department of Mathematics, University of Crete, Knossos Avenue, GR-714 09 Heraklion, Crete, Greece
autor
• Department of Applied Mathematics, University of Crete, Knossos Avenue, GR-714 09 Heraklion, Crete, Greece