External products of spectral metric spaces
Operator Algebras
2023-06-13 v2 K-Theory and Homology
Abstract
In this paper, we present a characterization of compact quantum metric spaces in terms of finite dimensional approximations. This characterization naturally leads to the introduction of a matrix analogue of a compact quantum metric space. As an application, we show that matrix compact quantum metric spaces are stable under minimal tensor products and more specifically that matrix spectral metric spaces are stable under the external product operation on unital spectral triples. We present several noncommutative examples of matrix compact quantum metric spaces.
Keywords
Cite
@article{arxiv.2304.03979,
title = {External products of spectral metric spaces},
author = {Jens Kaad},
journal= {arXiv preprint arXiv:2304.03979},
year = {2023}
}