Harmonic analysis approach to Gromov--Hausdorff convergence for   noncommutative tori
  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. 
Marius Junge, Sepideh Rezvani, Qiang Zeng
math.OA math-ph math.FA math.MP math.PR