Harmonic analysis approach to Gromov--Hausdorff convergence for noncommutative tori
Operator Algebras
2017-12-06 v2 Mathematical Physics
Functional Analysis
math.MP
Probability
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.
Keywords
Cite
@article{arxiv.1612.02735,
title = {Harmonic analysis approach to Gromov--Hausdorff convergence for noncommutative tori},
author = {Marius Junge and Sepideh Rezvani and Qiang Zeng},
journal= {arXiv preprint arXiv:1612.02735},
year = {2017}
}
Comments
81 pages, revised version to appear in CMP