Strongly $n$-supercyclic operators

Romuald Ernst (1)

1 Equipe Probabilités, Analyse et Statistique

In this paper, we are interested in the properties of a new class of operators, recently introduced by Shkarin, called strongly $n$-supercyclic operators. This notion is stronger than $n$-supercyclicity. We prove that such operators have interesting spectral properties and give examples and counter-examples answering some natural questions asked by Shkarin.

Mots clés: strongly n-supercyclic operators; n-supercyclic operators; n-supercyclicity; strong n-supercyclicity; linear operators; supercyclicity

Domaines: Analyse fonctionnelle [math.FA]

Romuald Ernst. Strongly $n$-supercyclic operators. 2012. ⟨hal-00697587v2⟩