A SOT-dense Path of Chaotic Operators with Same Hypercyclic Vectors

Document Type


Publication Date


Source Publication

Journal of Operator Theory


Recently many authors have obtained interesting results on the existence of a dense Gd set of common hypercyclic vectors for a path of operators. We show that on a separable infinite dimensional Hilbert space, there is a path of chaotic operators that is dense in the operator algebra with the strong operator topology, and yet each operator along the path has the exact same dense Gd set of hypercyclic vectors. As a corollary, the operators having that particular set of hypercyclic vectors form a connected subset of the operator algebra with the strong operator topology.


Journal of Operator Theory, Volume 66, No. 1, pp 107–124 (2011). Permalink: http://www.mathjournals.org/jot/2011-066-001/2011-066-001-003.pdf