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 Gδ 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 Gδ 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.