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

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arxiv 1612.02735 v2 pith:2YZEB2OG submitted 2016-12-08 math.OA math-phmath.FAmath.MPmath.PR

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

Marius Junge , Sepideh Rezvani , Qiang Zeng This is my paper
classification math.OA math-phmath.FAmath.MPmath.PR
keywords algebrasconvergencelipschitznoncommutativeresultstoriadditionalanalysis
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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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