Gromov-Hausdorff convergence of metric spaces of UCP maps
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915173236736000 |
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| author | Bhattacharyya, Tirthankar Duhan, Ritul Pradhan, Chandan |
| author_facet | Bhattacharyya, Tirthankar Duhan, Ritul Pradhan, Chandan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_15454 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Gromov-Hausdorff convergence of metric spaces of UCP maps Bhattacharyya, Tirthankar Duhan, Ritul Pradhan, Chandan Operator Algebras Functional Analysis 46L07, 46L87, 47C15, 47L25, 58B34 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. |
| title | Gromov-Hausdorff convergence of metric spaces of UCP maps |
| topic | Operator Algebras Functional Analysis 46L07, 46L87, 47C15, 47L25, 58B34 |
| url | https://arxiv.org/abs/2410.15454 |