Gromov-Hausdorff Distance for Quantum Metric Spaces

dc.creatorRieffel, Marc A.
dc.date2000-11-09
dc.date2003-02-20
dc.date.accessioned2026-07-07T04:38:31Z
dc.date.available2026-07-07T04:38:31Z
dc.descriptionBy 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, $A_þ$. We show, for consistently defined ``metrics'', that if a sequence $\{þ_n\}$ of parameters converges to a parameter $þ$, then the sequence $\{A_{þ_n}\}$ of quantum tori converges in quantum Gromov-Hausdorff distance to $A_þ$.
dc.description81 pages. Several minor improvements and several references added. To appear Memoirs Amer. Math. Soc
dc.identifierhttps://arxiv.org/abs/math/0011063
dc.identifierhttp://arxiv.org/abs/math/0011063
dc.identifierMem. Amer. Math. Soc. 168 (2004) no. 796, 1-65
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/60311
dc.subjectOperator Algebras
dc.subjectHigh Energy Physics - Theory
dc.subjectMetric Geometry
dc.subjectQuantum Physics
dc.subjectPrimary 46L87; Secondary 58B30, 60B10
dc.titleGromov-Hausdorff Distance for Quantum Metric Spaces
dc.typetext

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