Title

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

Document Type

Article

Language

eng

Format of Original

18 p.

Publication Date

2011

Publisher

Theta Foundation

Source Publication

Journal of Operator Theory

Source ISSN

0379-4024

Abstract

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.

Comments

Journal of Operator Theory, Vol. 66, No. 1 (2011): 107–124. Permalink.