PreprintarXiv licencearXiv
Typical dynamical properties of operators on ℓp
Abstract
We investigate the typical dynamical properties of hypercyclic operators in ℒM(X), the set of all bounded linear operators on X whose norms are at most M, when X=ℓp, 1< p<∞. We show that, with respect to SOT*, a typical operator T∈ ℒM(X) is weakly mixing, is weakly disjoint from a given hypercyclic operator S, is not topologically ergodic, and satisfies (T,T2,dotsc,Tk) is disjoint hypercyclic for any k≥ 2. We also show that the similar typical dynamical properties for the concrete family ℳ={I+Bw∈ ℒ(X): w∈ c0(ℤ)}, endowed with the norm topology, where Bw is a bilateral weighted backward shift.
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BibTeX
@misc{li2026typical,
title = {{Typical dynamical properties of operators on $\ell_p$}},
author = {Jian Li and Qijing Liao},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.10957},
eprint = {2609.10957},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.10957},
}
RIS
TY - UNPB
TI - Typical dynamical properties of operators on ℓ_p
AU - Jian Li
AU - Qijing Liao
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.10957
UR - https://arxiv.org/abs/2609.10957
AB - We investigate the typical dynamical properties of hypercyclic operators in ℒ_M(X), the set of all bounded linear operators on X whose norms are at most M, when X=ℓ_p, 1< p<∞. We show that, with respect to SOT^*, a typical operator T∈ ℒ_M(X) is weakly mixing, is weakly disjoint from a given hypercyclic operator S, is not topologically ergodic, and satisfies (T,T^2,dotsc,T^k) is disjoint hypercyclic for any k≥ 2. We also show that the similar typical dynamical properties for the concrete family ℳ={I+B_w∈ ℒ(X): w∈ c_0(ℤ)}, endowed with the norm topology, where B_w is a bilateral weighted backward shift.
ER -