%0 Journal Article
%T Γ-supercyclicity
%+ Institut de Mathématiques de Marseille (I2M)
%+ Laboratoire de Mathématiques de Lens (LML)
%A Charpentier, Stéphane
%A Ernst, Romuald
%A Menet, Quentin
%< avec comité de lecture
%@ 0022-1236
%J Journal of Functional Analysis
%I Elsevier
%V 270
%N 12
%P 4443-4465
%8 2016
%D 2016
%Z 1509.04912
%R 10.1016/j.jfa.2016.03.005
%K Hypercyclicity
%K Supercyclicity
%Z Mathematics [math]/Functional Analysis [math.FA]Journal articles
%X We characterize the subsets $\Gamma$ of $\C$ for which the notion of $\Gamma$-supercyclicity coincides with the notion of hypercyclicity, where an operator $T$ on a Banach space $X$ is said to be $\Gamma$-supercyclic if there exists $x\in X$ such that $\overline{\text{Orb}}(\Gamma x, T)=X$. In addition we characterize the sets $\Gamma \subset \C$ for which, for every operator $T$ on $X$, $T$ is hypercyclic if and only if there exists a vector $x\in X$ such that the set $\text{Orb}(\Gamma x, T)$ is somewhere dense in $X$. This extends results by Le\'on-M\"uller and Bourdon-Feldman respectively. We are also interested in the description of those sets $\Gamma \subset \C$ for which $\Gamma$-supercyclicity is equivalent to supercyclicity.
%G English
%2 https://hal.science/hal-01199885/document
%2 https://hal.science/hal-01199885/file/CEM-Gamma-supercyclicite.pdf
%L hal-01199885
%U https://hal.science/hal-01199885
%~ UNIV-ARTOIS
%~ CNRS
%~ UNIV-AMU
%~ EC-MARSEILLE
%~ I2M
%~ I2M-2014-
%~ LML