#### Document Type

Article

#### Publication Date

3-2011

#### Source Publication

Journal of Mathematical Analysis and Applications

#### Abstract

Given a separable, infinite dimensional Hilbert space, it was recently shown by the authors that there is a path of chaotic operators, which is dense in the operator algebra with the strong operator topology, and along which every operator has the exact same dense G_{δ} set of hypercyclic vectors. In the present work, we show that the conjugate set of any hypercyclic operator on a separable, infinite dimensional Banach space always contains a path of operators which is dense with the strong operator topology, and yet the set of common hypercyclic vectors for the entire path is a dense G_{δ} set. As a corollary, the hypercyclic operators on such a Banach space form a connected subset of the operator algebra with the strong operator topology.

## Comments

Post-print.

Journal of Mathematical Analysis and Applications, Volume 375, No. 1 (March 2011), DOI: 10.1016/j.jmaa.2010.08.018. Used with permission.