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