C*-algebraic quantum Gromov-Hausdorff distance

Details C*-algebraic quantum Gromov-Hausdorff distance C*-algebraic quantum Gromov-Hausdorff distance

2003-11-28

arxiv.org/abs/math/0312003v2

Mathematics

Operator Algebras

27 pages. Small modifications

Scientific paper

We introduce a new quantum Gromov-Hausdorff distance between C*-algebraic compact quantum metric spaces. Because it is able to distinguish algebraic structures, this new distance fixes a weakness of Rieffel's quantum distance. We show that this new quantum distance has properties analogous to the basic properties of the classical Gromov-Hausdorff distance, and we give criteria for when a parameterized family of C*-algebraic compact quantum metric spaces is continuous with respect to this new distance.

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