Hypercyclic Operators on Non-normable Fréchet Spaces

• DOI: 10.1006/jfan.1998.3315
• Publication Date: 2002-10-06T17:40:27Z
• Authors: José Bonet; Alfredo Peris
• Keywords: Operator (biology); Direct limit; Strictly singular operator

AbstractEvery infinite dimensional separable non-normable Fréchet space admits a continuous hypercyclic operator. A large class of separable countable inductive limits of Banach spaces with the same property is given, but an example of a separable complete inductive limit of Banach spaces which admits no hypercyclic operator is provided. It is also proved that no compact operator on a locally convex space is hypercyclic.