This is an announcement for the paper "On Read's type operators on Hilbert spaces" by Sophie Grivaux and Maria Roginskaya.
Abstract: Using Read's construction of operators without non-trivial invariant subspaces/subsets on $\ell_{1}$ 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 non-hypercyclic 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.
Archive classification: math.FA
Citation: Int. Math. Res. Not., 2008 Art. ID rnn083, 42 pp
Remarks: This is a preprint version of the article "On Read's type
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1301.6226
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