On Read's type operators on Hilbert spaces
Journal article, 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

Lille 1 University of Science and Technology

University of Gothenburg

Maria Roginskaya

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

International Mathematics Research Notices

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

Vol. 2008 1 rnn083

Subject Categories

Mathematical Analysis



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