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Compactness of composition operators on Hardy spaces of homogeneous rooted trees
Abstract
In this paper, we present a complete characterization of the compactness of arbitrary finite linear combinations of composition operators acting on Hardy spaces of homogeneous rooted trees. In particular, we obtain a characterization of compactness for linear combinations satisfying the CNC. As an application, we give an affirmative answer to a conjecture raised by Choe et al. [Trans. Amer. Math. Soc. Ser. B 9(2022), 733--756] concerning such Hardy spaces. Furthermore, we establish the phenomenon of (double) difference cancellation for linear combinations of composition operators by constructing explicit examples.
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BibTeX
@misc{liu2026compactness,
title = {{Compactness of composition operators on Hardy spaces of homogeneous rooted trees}},
author = {Lei Liu and Wanxin Ma},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.33717},
eprint = {2610.33717},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.33717},
}
RIS
TY - UNPB
TI - Compactness of composition operators on Hardy spaces of homogeneous rooted trees
AU - Lei Liu
AU - Wanxin Ma
PY - 2026
DA - 2026/10/24
PB - arXiv
DO - 10.48550/arxiv.2610.33717
UR - https://arxiv.org/abs/2610.33717
AB - In this paper, we present a complete characterization of the compactness of arbitrary finite linear combinations of composition operators acting on Hardy spaces of homogeneous rooted trees. In particular, we obtain a characterization of compactness for linear combinations satisfying the CNC. As an application, we give an affirmative answer to a conjecture raised by Choe et al. [Trans. Amer. Math. Soc. Ser. B 9(2022), 733--756] concerning such Hardy spaces. Furthermore, we establish the phenomenon of (double) difference cancellation for linear combinations of composition operators by constructing explicit examples.
ER -