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Communications in Mathematical Physics

, Volume 358, Issue 3, pp 919–994 | Cite as

Harmonic Analysis Approach to Gromov–Hausdorff Convergence for Noncommutative Tori

  • Marius Junge
  • Sepideh Rezvani
  • Qiang Zeng
Article
  • 83 Downloads

Abstract

We show that the rotation algebras are limits 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 Latrémolière, we use Lipschitz norms induced by the ‘carré du champ’ of certain natural dynamical systems, including the heat semigroup.

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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of IllinoisUrbanaUSA
  2. 2.Mathematics DepartmentNorthwestern UniversityEvanstonUSA

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