We define a metric on the class of metric spectral triples, which is null exactly between spectral triples with unitary equivalent Dirac operators and *-isomorphic underlying C*-algebras. This metric dominates the propinquity, and thus implies metric convergence of the compact quantum metric spaces induced by metric spectral triples. In the process of our construction, we also introduce the covariant modular propinquity, as a key component for the definition of the spectral propinquity.
- Pub Date:
- November 2018
- Mathematics - Operator Algebras;
- Mathematical Physics;
- 42 pages. Revised version corrects various typos, and adopts certain standard conventions about C*-correspondences