Recurrent Linear Operators
Functional Analysis
2015-09-01 v2 Dynamical Systems
Abstract
We study the notion of recurrence and some of its variations for linear operators acting on Banach spaces. We characterize recurrence for several classes of linear operators such as weighted shifts, composition operators and multiplication operators on classical Banach spaces. We show that on separable complex Hilbert spaces the study of recurrent operators reduces, in many cases, to the study of unitary operators. Finally, we study the notion of product recurrence and state some relevant open questions.
Cite
@article{arxiv.1301.1812,
title = {Recurrent Linear Operators},
author = {George Costakis and Antonios Manoussos and Ioannis Parissis},
journal= {arXiv preprint arXiv:1301.1812},
year = {2015}
}
Comments
38 pages; final version, incorporates referee's report; to appear in Complex Anal. Oper. Theory