|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'504'928
Articles rated: 2609
25 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
Gromov-Hausdorff Distance for Quantum Metric Spaces | | Marc A. Rieffel
; | | Date: |
9 Nov 2000 | | Journal: | Mem. Amer. Math. Soc. 168 (2004) no. 796, 1-65 | | Subject: | Operator Algebras; Metric Geometry MSC-class: Primary 46L87; Secondary 58B30, 60B10 | math.OA hep-th math.MG quant-ph | | Abstract: | 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, $A_{ h}$. We show, for consistently defined ``metrics’’, that if a sequence ${ h_n}$ of parameters converges to a parameter $ h$, then the sequence ${A_{ h_n}}$ of quantum tori converges in quantum Gromov-Hausdorff distance to $A_{ h}$. | | Source: | arXiv, math.OA/0011063 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER