Common Hypercyclic Vectors for the Conjugate Class of a Hypercyclic Operator

Authors

Kit C. Chan, Bowling Green State University - Main CampusFollow
Rebecca Sanders, Marquette UniversityFollow

Document Type

Article

Language

eng

Format of Original

10 p.

Publication Date

3-2011

Publisher

Elsevier

Source Publication

Journal of Mathematical Analysis and Applications

Source ISSN

0022-247X

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

Accepted version. Journal of Mathematical Analysis and Applications, Volume 375, No. 1 (March 2011). DOI. © 2011 Elsevier. Used with permission.

Recommended Citation

Chan, Kit C. and Sanders, Rebecca, "Common Hypercyclic Vectors for the Conjugate Class of a Hypercyclic Operator" (2011). Mathematics, Statistics and Computer Science Faculty Research and Publications. 18.
https://epublications.marquette.edu/mscs_fac/18