On Gromov-Hausdorff convergence for operator metric spaces
| dc.creator | Kerr, David | |
| dc.creator | Li, Hanfeng | |
| dc.date | 2004-11-08 | |
| dc.date | 2007-02-18 | |
| dc.date.accessioned | 2026-07-07T07:47:13Z | |
| dc.date.available | 2026-07-07T07:47:13Z | |
| dc.description | We introduce an analogue for Lip-normed operator systems of the second author's order-unit quantum Gromov-Hausdorff distance and prove that it is equal to the first author's complete distance. This enables us to consolidate the basic theory of what might be called operator Gromov-Hausdorff convergence. In particular we establish a completeness theorem and deduce continuity in quantum tori, Berezin-Toeplitz quantizations, and theta-deformations from work of the second author. We show that approximability by Lip-normed matrix algebras is equivalent to 1-exactness of the underlying operator space and, by applying a result of Junge and Pisier, that for n greater than or equal to 7 the set of isometry classes of n-dimensional Lip-normed operator systems is nonseparable. We also treat the question of generic complete order structure. | |
| dc.description | 23 pages; Section 7 added and Section 2 expanded; to appear in J. Operator Theory | |
| dc.identifier | https://arxiv.org/abs/math/0411157 | |
| dc.identifier | http://arxiv.org/abs/math/0411157 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/124090 | |
| dc.subject | Operator Algebras | |
| dc.subject | Metric Geometry | |
| dc.subject | 46L87, 53C23, 58B34, 46L07 | |
| dc.title | On Gromov-Hausdorff convergence for operator metric spaces | |
| dc.type | text |