The problem of completeness for Gromov-Hausdorff metrics on C*-algebras

Simple item page
dc.creatorGuido, Daniele
dc.creatorIsola, Tommaso
dc.date2005-02-01
dc.date2005-04-28
dc.date.accessioned2026-07-07T06:26:11Z
dc.date.available2026-07-07T06:26:11Z
dc.descriptionIt is proved that the family of equivalence classes of Lip-normed C*-algebras introduced by M. Rieffel, up to isomorphisms preserving the Lip-seminorm, is not complete w.r.t. the matricial quantum Gromov-Hausdorff distance introduced by D. Kerr. This is shown by exhibiting a Cauchy sequence whose limit, which always exists as an operator system, is not completely order isomorphic to any C*-algebra. Conditions ensuring the existence of a C*-structure on the limit are considered, making use of the notion of ultraproduct. More precisely, a necessary and sufficient condition is given for the existence, on the limiting operator system, of a C*-product structure inherited from the approximating C*-algebra. Such condition can be considered as a generalisation of the f-Leibniz conditions introduced by Kerr and Li. Furthermore, it is shown that our condition is not necessary for the existence of a C*-structure tout court, namely there are cases in which the limit is a C*-algebra, but the C*-structure is not inherited.
dc.description31 pages. Accepted for publication in Journal of Functional Analysis
dc.identifierhttps://arxiv.org/abs/math/0502013
dc.identifierhttp://arxiv.org/abs/math/0502013
dc.identifierJournal of Functional Analysis, 233 (2006) 173-205
dc.identifierdoi:10.1016/j.jfa.2005.04.007
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/97036
dc.subjectOperator Algebras
dc.subject46L87;53C23;58B34;46B08
dc.titleThe problem of completeness for Gromov-Hausdorff metrics on C*-algebras
dc.typetext

Files

Collections

arXiv