On Read's type operators on Hilbert spaces
Artikel i vetenskaplig tidskrift, 2008

Using Read's construction of operators without nontrivial invariant subspaces/subsets on l 1 or C 0 , we construct examples of operators on a Hilbert space whose set of hypercyclic vectors is "large" in various senses. We give an example of an operator such that the closure of every orbit is a closed subspace, and then, answering a question of D. Preiss, an example of an operator such that the set of its nonhypercyclic vectors is Gauss null. This operator has the property that it is orbit-unicellular, i.e. the family of the closures of its orbits is totally ordered. We also exhibit an example of an operator on a Hilbert space which is not orbit-reflexive. © The Author 2008. Published by Oxford University Press. All rights reserved.


Sophie Grivaux

Göteborgs universitet

Universite des Sciences et Technologies de Lille

Maria Roginskaya

Chalmers, Matematiska vetenskaper, Matematik

Göteborgs universitet

International Mathematics Research Notices

1073-7928 (ISSN) 1687-0247 (eISSN)


Matematisk analys