Title

Common Hypercyclic Vectors for the Unitary Orbit of a Hypercyclic Operator

Document Type

Article

Language

eng

Publication Date

3-1-2012

Publisher

Elsevier

Source Publication

Journal of Mathematical Analysis and Applications

Source ISSN

0022-247X

Abstract

For a separable, infinite dimensional Hilbert space, it was recently shown by the authors that the similarity orbit of a hypercyclic operator contains a path of operators which is dense in the operator algebra with the strong operator topology, and yet the set of common hypercyclic vectors for the entire path is a dense Gδ set. Motivated by that result, we show in the present paper that the unitary orbit of any hypercyclic operator contains a path of operators whose closure contains the entire unitary orbit with the strong operator topology, and yet every nonzero vector in the linear span of the orbit of a given hypercyclic vector is a common hypercyclic vector for the entire path.

Comments

Journal of Mathematical Analysis and Applications, Vol. 387, No. 1 (March 1, 2012): 17-23. DOI.

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