Spaces that admit hypercyclic operators with hypercyclic adjoints
Authors:
Henrik Petersson
Affiliation:
School of Mathematical Sciences, Chalmers/Göteborg University, SE-412 96, Göteborg, Sweden
Abstract:
A continuous linear operator is hypercyclic if there is an such that the orbit is dense. A result of H. Salas shows that any infinite-dimensional separable Hilbert space admits a hypercyclic operator whose adjoint is also hypercyclic. It is a natural question to ask for what other spaces does contain such an operator. We prove that for any infinite-dimensional Banach space with a shrinking symmetric basis, such as and any , there is an operator , where both and are hypercyclic.