dc.contributor.author
Antoine, R.
dc.contributor.author
Perera, F.
dc.contributor.author
Robert, L.
dc.contributor.author
Thiel, H.
dc.date.accessioned
2024-03-04T11:13:25Z
dc.date.accessioned
2024-09-19T14:29:09Z
dc.date.available
2024-03-04T11:13:25Z
dc.date.available
2024-09-19T14:29:09Z
dc.date.issued
2024-04-15
dc.identifier.uri
http://hdl.handle.net/2072/537455
dc.description.abstract
Using Cuntz semigroup techniques, we characterize when limit traces are dense in the space of all traces on a free ultrapower of a C*-algebra. More generally, we consider density of limit quasitraces on ultraproducts of C*-algebras. Quite unexpectedly, we obtain as an application that every simple C*-algebra that is (m,n)-pure in the sense of Winter is already pure. As another application, we provide a partial verification of the first Blackadar–Handelman conjecture on dimension functions. Crucial ingredients in our proof are new Hahn–Banach type separation theorems for noncancellative cones, which in particular apply to the cone of extended-valued traces on a C*-algebra. © 2024
eng
dc.description.sponsorship
The two first named authors were partially supported by the Spanish State Research Agency (grants No. MTM2017-83487-P and PID2020-113047GB-I00/AEI/10.13039/501100011033 ), by the Comissionat per Universitats i Recerca de la Generalitat de Catalunya (grant No. 2017-SGR-1725 ) and by the Spanish State Research Agency through the Severo Ochoa and María de Maeztu Program for Centers and Units of Excellence in R&D ( CEX2020-001084-M ). The fourth named author was partially supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy EXC 2044-390685587 (Mathematics Münster: Dynamics-Geometry-Structure), by the ERC Consolidator Grant No. 681207 , and by the Knut and Alice Wallenberg Foundation (KAW 2021.0140 ).
dc.format.extent
65 p.
cat
dc.publisher
Academic Press Inc.
cat
dc.relation.ispartof
Journal of Functional Analysis
cat
dc.rights
L'accés als continguts d'aquest document queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons: https://creativecommons.org/licenses/by/4.0/
dc.source
RECERCAT (Dipòsit de la Recerca de Catalunya)
dc.subject.other
C<sup>⁎</sup>-algebras; Cuntz semigroups; Traces; Ultraproducts
cat
dc.title
Traces on ultrapowers of C*-algebras
cat
dc.type
info:eu-repo/semantics/article
cat
dc.type
info:eu-repo/semantics/publishedVersion
cat
dc.identifier.doi
10.1016/j.jfa.2024.11034110.1016/j.jfa.2024.110341
cat
dc.rights.accessLevel
info:eu-repo/semantics/openAccess
