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On the dynamics of weighted shifts on Fréchet sequence spaces over trees
Abstract
In this paper, we give characterizations of Li--Yorke chaos, mean Li--Yorke chaos and distributional chaos for weighted backward shifts acting on general Fréchet sequence spaces over directed trees. As corollaries, we obtain explicit characterizations in the setting of Köthe spaces λp(A,V), where p∈{0}∪[1,∞) and V is a directed tree. In particular, we obtain criteria for the case of the classical Banach spaces ℓp(V), p∈[1,∞), and c0(V).
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BibTeX
@misc{azevedo2026dynamics,
title = {{On the dynamics of weighted shifts on Fréchet sequence spaces over trees}},
author = {Mateus Azevedo and Fernando Costa Jr. and João V. A. Pinto},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.10053},
eprint = {2611.10053},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.10053},
}
RIS
TY - UNPB
TI - On the dynamics of weighted shifts on Fréchet sequence spaces over trees
AU - Mateus Azevedo
AU - Fernando Costa Jr.
AU - João V. A. Pinto
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.10053
UR - https://arxiv.org/abs/2611.10053
AB - In this paper, we give characterizations of Li--Yorke chaos, mean Li--Yorke chaos and distributional chaos for weighted backward shifts acting on general Fréchet sequence spaces over directed trees. As corollaries, we obtain explicit characterizations in the setting of Köthe spaces λ_p(A,V), where p∈{0}∪[1,∞) and V is a directed tree. In particular, we obtain criteria for the case of the classical Banach spaces ℓ^p(V), p∈[1,∞), and c_0(V).
ER -