Home OALib Journal OALib PrePrints Submit Ranking News My Lib FAQ About Us Follow Us+
 All Title Author Keywords Abstract
 Publish in OALib Journal ISSN: 2333-9721 APC: Only \$99

 Relative Articles Quantum Metric Spaces and the Gromov-Hausdorff Propinquity Computing the Gromov-Hausdorff Distance for Metric Trees Topographic Gromov-Hausdorff quantum Hypertopology for Quantum Proper Metric Spaces The Gromov-Hausdorff Metric on the Space of Compact Metric Spaces is Strictly Intrinsic Quantized Gromov-Hausdorff distance Gromov-Hausdorff Approximation of Metric Spaces with Linear Structure On Gromov-Hausdorff convergence for operator metric spaces C*-algebraic quantum Gromov-Hausdorff distance A note on Gromov-Hausdorff-Prokhorov distance between (locally) compact measure spaces Vector bundles and Gromov-Hausdorff distance More...
Mathematics  2000

# Gromov-Hausdorff Distance for Quantum Metric Spaces

 Full-Text   Cite this paper

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_{\th}\$. We show, for consistently defined ``metrics'', that if a sequence \$\{\th_n\}\$ of parameters converges to a parameter \$\th\$, then the sequence \$\{A_{\th_n}\}\$ of quantum tori converges in quantum Gromov-Hausdorff distance to \$A_{\th}\$.

Full-Text