ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

1991 MS Classification: 46,47 Bonet, José, , Peris, Alfredo, Universidad Politécnica de Valencia, Spain Hypercyclic operators on non-normable Fréchet spaces S. Ansari and L. Bernal proved independently in 1997 that every infinitedimensional, separable Banach space admits a continuous, linear, hypercyclic operator. An operator is hypercyclic if there is a vector in the space with a dense orbit. We show that every infinite-dimensional, separable and non-normable Fréchet space admits a continuous, linear hypercyclic operator too. 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. No compact operator on a locally convex space is hypercyclic. These results are joint work with A. Peris.