Dynamics of Weighted Backward Shifts on Cesàro Spaces of Rooted Trees
Abstract
We study the dynamics of weighted backward shifts on Ces`aro spaces associated with leafless locally finite rooted trees. We first characterize their boundedness in terms of adjacent level cardinalities and edge weights. We then characterize their ℱ-transitivity by a growth condition involving level cardinalities, products of weights along paths, and a level-dependent Ces`aro factor. As consequences, we obtain criteria for hypercyclicity, weak mixing, topological ergodicity, and topological mixing. We also characterize the existence of nonzero orbit limit points and chaotic weighted shifts, the latter in terms of normalized fixed points and unit flows satisfying an explicit summability condition. Examples show that ℱunderlined>0-transitivity need not imply frequent hypercyclicity, that a nonhypercyclic weighted shift may nevertheless have a nonzero orbit limit point, and that topological mixing need not imply chaos.
Related
- Weighted Cesàro type operators on the weighted Bergman spaces in the unit ball
- On sharp constants for infinitely many equivalent norms on Cesàro function spaces
- Integral Operators on Fractional Cesàro--Morrey Spaces over ℚp
- Cesàro-type operators on average radial integrability spaces induced by doubling weights
- ℱ-Transitivity of Backward Shifts on Lattice Graphs
BibTeX
@misc{chen2026dynamics,
title = {{Dynamics of Weighted Backward Shifts on Cesàro Spaces of Rooted Trees}},
author = {Xiang Chen and Meng-Huan Cheng and Liang Zhang and Ze-Hua Zhou},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.21752},
eprint = {2609.21752},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.21752},
}
RIS
TY - UNPB
TI - Dynamics of Weighted Backward Shifts on Cesàro Spaces of Rooted Trees
AU - Xiang Chen
AU - Meng-Huan Cheng
AU - Liang Zhang
AU - Ze-Hua Zhou
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2609.21752
UR - https://arxiv.org/abs/2609.21752
AB - We study the dynamics of weighted backward shifts on Ces`aro spaces associated with leafless locally finite rooted trees. We first characterize their boundedness in terms of adjacent level cardinalities and edge weights. We then characterize their ℱ-transitivity by a growth condition involving level cardinalities, products of weights along paths, and a level-dependent Ces`aro factor. As consequences, we obtain criteria for hypercyclicity, weak mixing, topological ergodicity, and topological mixing. We also characterize the existence of nonzero orbit limit points and chaotic weighted shifts, the latter in terms of normalized fixed points and unit flows satisfying an explicit summability condition. Examples show that ℱ_underlined>0-transitivity need not imply frequent hypercyclicity, that a nonhypercyclic weighted shift may nevertheless have a nonzero orbit limit point, and that topological mixing need not imply chaos.
ER -