Baire theorem and hypercyclic algebras
Functional Analysis
2020-09-17 v2
Abstract
The question of whether a hypercyclic operator acting on a Fr{\'e}chet algebra admits or not an algebra of hypercyclic vectors (but 0) has been addressed in the recent literature. In this paper we give new criteria and characterizations in the context of convolution operators acting on and backward shifts acting on a general Fr{\'e}chet sequence algebra.Analogous questions arise for stronger properties like frequent hypercyclicity. In this trend we give a sufficient condition for a weighted backward shift to admit an upper frequently hypercyclic algebra and we find a weighted backward shift acting on admitting a frequently hypercyclic algebra for the coordinatewise product. The closed hypercyclic algebra problem is also covered.
Keywords
Cite
@article{arxiv.1910.05000,
title = {Baire theorem and hypercyclic algebras},
author = {Frédéric Bayart and Fernando Costa Júnior and Dimitris Papathanasiou},
journal= {arXiv preprint arXiv:1910.05000},
year = {2020}
}