Bunce-Deddens Algebras as Quantum Gromov-Hausdorff Distance Limits of Circle Algebras

被引：3
|
作者：
Aguilar, Konrad [1 ]
Latremoliere, Frederic [2 ]
Rainone, Timothy [3 ]
机构：
[1] Pomona Coll, Dept Math & Stat, 610 N Coll Ave, Claremont, CA 91711 USA
[2] Univ Denver, Dept Math, Denver, CO 80208 USA
[3] Occidental Coll, Dept Math, Los Angeles, CA 90041 USA
来源：
INTEGRAL EQUATIONS AND OPERATOR THEORY | 2022年 / 94卷 / 01期
基金：
欧盟地平线“2020”;
关键词：
Noncommutative metric geometry; Gromov-Hausdorff convergence; Monge-Kantorovich distance; Quantum Metric Spaces; Lipnorms; Bunce-Deddens algebras; AT-algebras; SPACES;
D O I：
10.1007/s00020-021-02678-w
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We show that Bunce-Deddens algebras, which are AT-algebras, are also limits of circle algebras for Rieffel's quantum Gromov-Hausdorff distance, and moreover, form a continuous family indexed by the Baire space. To this end, we endow Bunce-Deddens algebras with a quantum metric structure, a step which requires that we reconcile the constructions of the Latr ' emoli`ere's Gromov-Hausdorff propinquity and Rieffel's quantum Gromov-Hausdorff distance when working on order-unit quantum metric spaces. This work thus continues the study of the connection between inductive limits and metric limits.
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页数：42
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