Gromov-Hausdorff convergence of metric spaces of UCP maps

Autor: Bhattacharyya, Tirthankar, Duhan, Ritul, Pradhan, Chandan
Rok vydání: 2024
Předmět:
Druh dokumentu: Working Paper
Popis: It is shown that van Suijlekom's technique of imposing a set of conditions on operator system spectral triples ensures Gromov-Hausdorff convergence of sequences of sets of unital completely positive maps (equipped with the BW-topology which is metrizable). This implies that even when only a part of the spectrum of the Dirac operator is available together with a certain truncation of the $C^*$-algebra, information about the geometry can be extracted.
Databáze: arXiv