PreprintCC0arXiv
Characterisations for coarse embeddability via quasi-locality and Schur multipliers
Abstract
We establish three new characterisations of coarse embeddability into Hilbert space for discrete metric spaces of bounded geometry in terms of escaping quasi-local couplings, Schur multipliers, and operator norm state localisation. As applications, we prove that if a sparse metric space of bounded geometry is coarsely embeddable into Hilbert space, then every ghost projection in the quasi-local algebra is compact, while we also provide a counterexample to the converse implication. Finally, we characterise coarse embeddability into Hilbert space via the relative Haagerup property for the quasi-local algebra, and investigate its relation to coarse embeddability into ℓp for p>2.
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BibTeX
@misc{li2026characterisations,
title = {{Characterisations for coarse embeddability via quasi-locality and Schur multipliers}},
author = {Kang Li and Jiawen Zhang and Jingming Zhu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.21632},
eprint = {2610.21632},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.21632},
note = {CC0},
}
RIS
TY - UNPB
TI - Characterisations for coarse embeddability via quasi-locality and Schur multipliers
AU - Kang Li
AU - Jiawen Zhang
AU - Jingming Zhu
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.21632
UR - https://arxiv.org/abs/2610.21632
AB - We establish three new characterisations of coarse embeddability into Hilbert space for discrete metric spaces of bounded geometry in terms of escaping quasi-local couplings, Schur multipliers, and operator norm state localisation. As applications, we prove that if a sparse metric space of bounded geometry is coarsely embeddable into Hilbert space, then every ghost projection in the quasi-local algebra is compact, while we also provide a counterexample to the converse implication. Finally, we characterise coarse embeddability into Hilbert space via the relative Haagerup property for the quasi-local algebra, and investigate its relation to coarse embeddability into ℓ^p for p>2.
ER -