Gromov-Hausdorff Distance for Quantum Metric Spaces
| dc.creator | Rieffel, Marc A. | |
| dc.date | 2000-11-09 | |
| dc.date | 2003-02-20 | |
| dc.date.accessioned | 2026-07-07T04:38:31Z | |
| dc.date.available | 2026-07-07T04:38:31Z | |
| dc.description | By a quantum metric space we mean a C^*-algebra (or more generally an order-unit space) equipped with a generalization of the Lipschitz seminorm on functions which is defined by an ordinary metric. We develop for compact quantum metric spaces a version of Gromov-Hausdorff distance. We show that the basic theorems of the classical theory have natural quantum analogues. Our main example involves the quantum tori, $A_þ$. We show, for consistently defined ``metrics'', that if a sequence $\{þ_n\}$ of parameters converges to a parameter $þ$, then the sequence $\{A_{þ_n}\}$ of quantum tori converges in quantum Gromov-Hausdorff distance to $A_þ$. | |
| dc.description | 81 pages. Several minor improvements and several references added. To appear Memoirs Amer. Math. Soc | |
| dc.identifier | https://arxiv.org/abs/math/0011063 | |
| dc.identifier | http://arxiv.org/abs/math/0011063 | |
| dc.identifier | Mem. Amer. Math. Soc. 168 (2004) no. 796, 1-65 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/60311 | |
| dc.subject | Operator Algebras | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Metric Geometry | |
| dc.subject | Quantum Physics | |
| dc.subject | Primary 46L87; Secondary 58B30, 60B10 | |
| dc.title | Gromov-Hausdorff Distance for Quantum Metric Spaces | |
| dc.type | text |