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Gromov-Hausdorff Convergence of Spectral Truncations for Noncommutative Tori
Abstract
We prove the Gromov-Hausdorff convergence of the state spaces, equipped with Connes' distance function, of the operator systems associated with spectral truncations for noncommutative n-tori, n≥ 2. The action of the n-torus on the noncommutative n-torus, together with an appropriate use of Bochner integrals, enables us to construct an C1-approximate order isomorphism that establishes the convergence. The earlier convergence result for the classical case of tori [20] follows as a special case of our result. We conclude by studying the C*-envelopes and propagation numbers of the truncated operator systems and show that the structural properties of the truncated operator systems for tori persist under deformation.
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BibTeX
@misc{bhatt2026gromovhausdorff,
title = {{Gromov-Hausdorff Convergence of Spectral Truncations for Noncommutative Tori}},
author = {Vibhor Bhatt and Satyajit Guin and Palash Sharma},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.01132},
eprint = {2610.01132},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.01132},
}
RIS
TY - UNPB
TI - Gromov-Hausdorff Convergence of Spectral Truncations for Noncommutative Tori
AU - Vibhor Bhatt
AU - Satyajit Guin
AU - Palash Sharma
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.01132
UR - https://arxiv.org/abs/2610.01132
AB - We prove the Gromov-Hausdorff convergence of the state spaces, equipped with Connes' distance function, of the operator systems associated with spectral truncations for noncommutative n-tori, n≥ 2. The action of the n-torus on the noncommutative n-torus, together with an appropriate use of Bochner integrals, enables us to construct an C^1-approximate order isomorphism that establishes the convergence. The earlier convergence result for the classical case of tori [20] follows as a special case of our result. We conclude by studying the C^*-envelopes and propagation numbers of the truncated operator systems and show that the structural properties of the truncated operator systems for tori persist under deformation.
ER -