2015/09/16 by Charpentier, Stéphane, Ernst, Romuald, Menet, Quentin
#FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.1509.04912
We characterize the subsets Γ of \C for which the notion of Γ-supercyclicity coincides with the notion of hypercyclicity, where an operator T on a Banach space X is said to be Γ-supercyclic if there exists x∈ X such that Orb(Γx, T)=X. In addition we characterize the sets Γ⊂ \C for which, for every operator T on X, T is hypercyclic if and only if there exists a vector x∈ X such that the set Orb(Γx, T) is somewhere dense in X. This extends results by León-Müller and Bourdon-Feldman respectively. We are also interested in the description of those sets Γ⊂ \C for which Γ-supercyclicity is equivalent to supercyclicity.