Quantized Gromov-Hausdorff distance

dc.creatorWu, Wei
dc.date2005-03-16
dc.date2005-03-29
dc.date.accessioned2026-07-07T12:30:48Z
dc.date.available2026-07-07T12:30:48Z
dc.descriptionA 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.description34 pages. An oversight appeared in Proposition 4.9 of Version 1. This proposition has been deleted. Also some type errors have been corrected
dc.identifierhttps://arxiv.org/abs/math/0503344
dc.identifierhttp://arxiv.org/abs/math/0503344
dc.identifierJ. Funct. Anal. 238 (2006), no. 1, 58--98
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/216245
dc.subjectOperator Algebras
dc.subjectMetric Geometry
dc.subject46L87; 46L07; 53C23; 58B34; 60B10
dc.titleQuantized Gromov-Hausdorff distance
dc.typetext

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