Non-existence of frequently hypercyclic subspaces for P(D)

Frédéric Bayart (1) , Romuald Ernst (2, 3) , Quentin Menet (4)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal
2 I2M - Institut de Mathématiques de Marseille
3 LMPA - Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville
4 Institut de Mathématiques [Mons]

We answer a question posed by Bonilla and Grosse-Erdmann by showing that the operators P(D) on the space of entire functions H(C), where D is the differentiation operator and P is a polynomial, do not possess a frequently hypercyclic subspace.

Mots clés: WEIGHTED SHIFTS; BANACH-SPACES; OPERATORS; INVARIANT; VECTORS; MANIFOLDS; SPECTRUM; THEOREM

Domaines: Analyse fonctionnelle [math.FA]

Frédéric Bayart, Romuald Ernst, Quentin Menet. Non-existence of frequently hypercyclic subspaces for P(D). Israel Journal of Mathematics, 2016, 214 (1), pp.149 - 166. ⟨10.1007/s11856-016-1352-3⟩. ⟨hal-01486846⟩