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arXiv · 1612.02735

Harmonic analysis approach to Gromov--Hausdorff convergence for noncommutative tori

Marius Junge·Sepideh Rezvani·Qiang Zeng
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Abstract

We show that the rotation algebras are limit of matrix algebras in a very strong sense of convergence for algebras with additional Lipschitz structure. Our results generalize to higher dimensional noncommutative tori and operator valued coefficients. In contrast to previous results by Rieffel, Li, Kerr, and Latr\'emoli\`ere we use Lipschitz norms induced by the `carr\'e du champ' of certain natural dynamical systems, including the heat semigroup.

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Marius Junge, Sepideh Rezvani, Qiang Zeng. 2016-12-08. Harmonic analysis approach to Gromov--Hausdorff convergence for noncommutative tori. https://doi.org/10.1007/s00220-017-3017-4

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