Matricial quantum Gromov-Hausdorff distance

Details Matricial quantum Gromov-Hausdorff distance Matricial quantum Gromov-Hausdorff distance

2002-07-30

arxiv.org/abs/math/0207282v1

Mathematics

Operator Algebras

29 pages

Scientific paper

We develop a matricial version of Rieffel's Gromov-Hausdorff distance for compact quantum metric spaces within the setting of operator systems and unital C*-algebras. Our approach yields a metric space of ``isometric'' unital complete order isomorphism classes of metrized operator systems which in many cases exhibits the same convergence properties as those in the quantum metric setting, as for example in Rieffel's approximation of the sphere by matrix algebras using Berezin quantization. Within the metric subspace of metrized unital C*-algebras we establish the convergence of sequences which are Cauchy with respect to a larger Leibniz distance, and we also prove an analogue of the precompactness theorems of Gromov and Rieffel.

Affiliated with

Also associated with

No associations

Rating

Matricial quantum Gromov-Hausdorff distance does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Matricial quantum Gromov-Hausdorff distance, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Matricial quantum Gromov-Hausdorff distance will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-357147