Trichotomy for the orbits of a hypercyclic operator on a Banach space
Functional Analysis
2024-10-22 v1 Dynamical Systems
Abstract
We obtain a trichotomy for the orbits of a hypercyclic operator on a separable Banach space : (1) every vector is mean asymptotic to zero; (2) generic vectors are absolutely mean irregular; (3) every hypercyclic vector is mean divergent to infinity. Examples of weighted backward shifts on show that all three cases can happen.
Cite
@article{arxiv.2407.07214,
title = {Trichotomy for the orbits of a hypercyclic operator on a Banach space},
author = {Jian Li},
journal= {arXiv preprint arXiv:2407.07214},
year = {2024}
}
Comments
12 papers,to appear in Proc. Amer. Math. Soc