Order-unit quantum Gromov-Hausdorff distance

摘要

We introduce a new distance dist(oq) between compact quantum metric spaces. We show that distoq is Lipschitz equivalent to Rieffel's distance dist(q), and give criteria for when a parameterized family of compact quantum metric spaces is continuous with respect to distoq. As applications, we show that the continuity of a parameterized family of quantum metric spaces induced by ergodic actions of a fixed compact group is determined by the multiplicities of the actions, generalizing Rieffel's work on noncommutative tori and integral coadjoint orbits of semisimple compact connected Lie groups; we also show that the theta-deformations of Connes and Landi are continuous in the parameter theta. (c) 2005 Elsevier Inc. All rights reserved.