Somewhere dense Cesàro orbits and rotations of Cesàro hypercyclic operators

• Autorzy: George Costakis , Demetris Hadjiloucas
• Języki publikacji: 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.

Kategorie tematyczne

• 47A16: Cyclic vectors, hypercyclic and chaotic operators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2006
• Tom: 175
• Numer: 3
• Strony: 249-269

Daty

wydano

2006

Twórcy

autor

George Costakis

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

autor

Demetris Hadjiloucas

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

Identyfikatory

DOI

10.4064/sm175-3-4