Juan Bes, Bowling Green University Ohio USA

Operators with common Hypercyclic subspaces

(Joint with R. Aron, F. Leon and A. Peris)

Let T be a bounded operator on a Banach space X. A vector x in X is said to be hypercyclic for T provided the orbit {x, T x, T^{2}x, … } is dense in X. We consider conditions for a family of operators acting on X to have a common hypercyclic subspace, that is, to have a closed subspace of infinite dimension consisting entirely, except for the origin, of vectors that are hypercyclic for each operator in the family. Our work complements recent results by G. Costakis and M. Sambarino and by F. Bayart.