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arXiv · 2610.21632

Characterisations for coarse embeddability via quasi-locality and Schur multipliers

Kang Li·Jiawen Zhang·Jingming Zhu
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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 $\ell^p$ for $p>2$.

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Kang Li, Jiawen Zhang, Jingming Zhu. 2026-10-21. Characterisations for coarse embeddability via quasi-locality and Schur multipliers. https://arxiv.org/abs/2610.21632

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