Traces on ultrapowers of C*-algebras
| Autor: | Antoine, Ramon, Perera, Francesc, Robert, Leonel, Thiel, Hannes |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 47 pages; minor changes, included further references |
| Databáze: | arXiv |
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