Publication Date
10-15-2012
Document Type
Article
Keywords
Noncommutative metric geometry, Monge-Kantorovich distance, Non-unital C*-algebras, Quantum Metric Spaces, Lip-norms, Moyal planes
Abstract
We introduce the notion of a quantum locally compact metric space, which is the noncommutative analogue of a locally compact metric space, and generalize to the non-unital setting the notion of quantum metric spaces introduced by Rieffel. We then provide several examples of such structures, including the Moyal plane, compact quantum metric spaces and locally compact metric spaces. This paper provides an answer to the question raised in the literature about the proper notion of a quantum metric space in the nonunital setup and offers important insights into noncommutative geometry for non compact quantum spaces.
Recommended Citation
Latrémolière, F. (2012). Quantum Locally Compact Metric Spaces. Mathematics Preprint Series. Retrieved from https://digitalcommons.du.edu/math_preprints/27
Comments
The published version of this article, published in the Journal of Functional Analysis, is available online at: https://doi.org/10.1016/j.jfa.2012.10.016