TY - JOUR
T1 - Harmonic Analysis Approach to Gromov–Hausdorff Convergence for Noncommutative Tori
AU - Junge, Marius
AU - Rezvani, Sepideh
AU - Zeng, Qiang
N1 - Publisher Copyright:
© 2017, Springer-Verlag GmbH Germany.
PY - 2018/3/1
Y1 - 2018/3/1
N2 - 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.
AB - 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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U2 - 10.1007/s00220-017-3017-4
DO - 10.1007/s00220-017-3017-4
M3 - Article
AN - SCOPUS:85032944848
SN - 0010-3616
VL - 358
SP - 919
EP - 994
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
IS - 3
ER -