AMS eBook CollectionsOne of the world's most respected mathematical collections, available in digital format for your library or institution
Gromov-Hausdorff distance for quantum metric spaces
About this Title
Marc A. Rieffel
Publication: Memoirs of the American Mathematical Society
Publication Year:
2004; Volume 168, Number 796
ISBNs: 978-0-8218-3518-0 (print); 978-1-4704-0394-2 (online)
DOI: https://doi.org/10.1090/memo/0796
MathSciNet review: 2055927
MSC: Primary 46L87; Secondary 53C23, 58B34, 60B10
Table of Contents
Chapters
- Gromov-Hausdorff distance for quantum metric spaces
- 1. Introduction
- 2. Compact quantum metric spaces
- 3. Quotients (= “subsets”)
- 4. Quantum Gromov-Hausdorff distance
- 5. Bridges
- 6. Isometries
- 7. Distance zero
- 8. Actions of compact groups
- 9. Quantum tori
- 10. Continuous fields of order-unit spaces
- 11. Continuous fields of lip-norms
- 12. Completeness
- 13. Finite approximation and compactness
- Matrix algebras converge to the sphere for quantum Gromov-Hausdorff distance
- 0. Introduction
- 1. The quantum metric spaces
- 2. Choosing the bridge constant $\gamma$
- 3. Compact semisimple Lie groups
- 4. Covariant symbols
- 5. Contravariant symbols
- 6. Conclusion of the proof of Theorem 3.2