Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

Somewhere dense Cesàro orbits and rotations of Cesàro hypercyclic operators

100%

Costakis G., Hadjiloucas D.

Studia Mathematica

2006

tom 175

nr 3

249-269

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.

Ograniczanie wyników

1 Studia Mathematica

1 Costakis G.

1 Hadjiloucas D.

1 2006

Wyniki wyszukiwania

Somewhere dense Cesàro orbits and rotations of Cesàro hypercyclic operators