Order-unit quantum Gromov-Hausdorff distance
Abstract
Description
We introduce a new distance dist_oq between compact quantum metric spaces. We show that dist_oq 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 dist_oq. 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.
42 pages. Proposition 4.7 is added. To apear in J. Funct. Anal
42 pages. Proposition 4.7 is added. To apear in J. Funct. Anal