Disjoint and common hypercyclic algebras

Frédéric Bayart (1) , Fernando Costa , Dimitris Papathanasiou

1 LMBP - Laboratoire de Mathématiques Blaise Pascal

Over time the concept of hypercyclicity has been explored in different manners and contexts, gaining new forms and applications. In particular when the space has an adjacent structure, we can always look for sets of hypercyclic vectors compatible with that framework. In this paper we deal with hypercyclic operators acting on Fréchet sequence algebras and give criteria for the existence of common and disjoint hypercyclic algebras.

Mots clés: hypercyclic operators weighted shifts convolution operators hypercyclic algebras; hypercyclic operators; weighted shifts; convolution operators; hypercyclic algebras

Domaines: Analyse fonctionnelle [math.FA]

Frédéric Bayart, Fernando Costa, Dimitris Papathanasiou. Disjoint and common hypercyclic algebras. Israel Journal of Mathematics, 2022, 250 (1), pp.211-264. ⟨10.1007/s11856-022-2337-z⟩. ⟨hal-03903487⟩