Quantized Gromov-Hausdorff distance
| dc.creator | Wu, Wei | |
| dc.date | 2005-03-16 | |
| dc.date | 2005-03-29 | |
| dc.date.accessioned | 2026-07-07T12:30:48Z | |
| dc.date.available | 2026-07-07T12:30:48Z | |
| dc.description | A quantized metric space is a matrix order unit space equipped with an operator space version of Rieffel's Lip-norm. We develop for quantized metric spaces an operator space version of quantum Gromov-Hausdorff distance. We show that two quantized metric spaces are completely isometric if and only if their quantized Gromov-Hausdorff distance is zero. We establish a completeness theorem. As applications, we show that a quantized metric space with 1-exact underlying matrix order unit space is a limit of matrix algebras with respect to quantized Gromov-Hausdorff distance, and that matrix algebras converge naturally to the sphere for quantized Gromov-Hausdorff distance. | |
| dc.description | 34 pages. An oversight appeared in Proposition 4.9 of Version 1. This proposition has been deleted. Also some type errors have been corrected | |
| dc.identifier | https://arxiv.org/abs/math/0503344 | |
| dc.identifier | http://arxiv.org/abs/math/0503344 | |
| dc.identifier | J. Funct. Anal. 238 (2006), no. 1, 58--98 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/216245 | |
| dc.subject | Operator Algebras | |
| dc.subject | Metric Geometry | |
| dc.subject | 46L87; 46L07; 53C23; 58B34; 60B10 | |
| dc.title | Quantized Gromov-Hausdorff distance | |
| dc.type | text |