Subspace hypercyclicity
Abstract
A bounded linear operator T on Hilbert space is subspacehypercyclic for a subspace M if there exists a vector whose orbit under T intersects the subspace in a relatively dense set. We construct examples to show that subspacehypercyclicity is interesting, including a nontrivial subspacehypercyclic operator that is not hypercyclic. There is a Kitailike criterion that implies subspacehypercyclicity and although the spectrum of a subspacehypercyclic operator must intersect the unit circle, not every component of the spectrum will do so. We show that, like hypercyclicity, subspacehypercyclicity is a strictly infinitedimensional phenomenon. Additionally, compact or hyponormal operators can never be subspacehypercyclic.
 Publication:

arXiv eprints
 Pub Date:
 January 2010
 arXiv:
 arXiv:1001.5320
 Bibcode:
 2010arXiv1001.5320M
 Keywords:

 Mathematics  Functional Analysis;
 Mathematics  Dynamical Systems;
 47A16
 EPrint:
 15 pages