2002/07/30 by David Kerr, Kerr, David · 1 citation
Mathematics · #FOS: Mathematics #Metric Geometry (math.MG) #Operator Algebras (math.OA) #math.MG #math.OA
paper · pdf · doi:10.48550/arxiv.math/0207282
29 pages
arxiv created 2002/07/30 · arxiv updated 2009/11/30
We develop a matricial version of Rieffel's Gromov-Hausdorff distance for compact quantum metric spaces within the setting of operator systems and unital C*-algebras. Our approach yields a metric space of ``isometric'' unital complete order isomorphism classes of metrized operator systems which in many cases exhibits the same convergence properties as those in the quantum metric setting, as for example in Rieffel's approximation of the sphere by matrix algebras using Berezin quantization. Within the metric subspace of metrized unital C*-algebras we establish the convergence of sequences which are Cauchy with respect to a larger Leibniz distance, and we also prove an analogue of the precompactness theorems of Gromov and Rieffel.