A Note on the Perturbations of Compact Quantum Metric Spaces  

作　　者：Li Guang WANG 

机构地区：[1]School of Mathematical Sciences,Qufu Normal University

出　　处：《Acta Mathematica Sinica,English Series》2016年第10期1214-1220,共7页数学学报（英文版）

基　　金：Supported in part by NSFC(Grant No.11371222)

摘　　要：In this short note, we consider the perturbation of compact quantum metric spaces. We first show that for two compact quantum metric spaces （A, P） and （B, Q） for which A and B are subspaces of an order-unit space t and P and Q are Lip-norms on A and B respectively, the quantum Gromov-Hausdorff distance between （A, P） and （B, Q） is small under certain conditions. Then some other perturbation results on compact quantum metric spaces derived from spectral triples are also given.In this short note, we consider the perturbation of compact quantum metric spaces. We first show that for two compact quantum metric spaces （A, P） and （B, Q） for which A and B are subspaces of an order-unit space t and P and Q are Lip-norms on A and B respectively, the quantum Gromov-Hausdorff distance between （A, P） and （B, Q） is small under certain conditions. Then some other perturbation results on compact quantum metric spaces derived from spectral triples are also given.

关 键 词：Compact quantum metric space quantum Gromov-Hausdorff distance C＊-algebra Lip-norm spectral triple 

分 类 号：O189.11[理学—数学] O413[理学—基础数学]