The cone of lower semicontinuous traces on a C*-algebra
| dc.creator | Elliott, George A. | |
| dc.creator | Robert, Leonel | |
| dc.creator | Santiago, Luis | |
| dc.date | 2008-05-20 | |
| dc.date | 2009-01-21 | |
| dc.date.accessioned | 2026-07-07T12:31:46Z | |
| dc.date.available | 2026-07-07T12:31:46Z | |
| dc.description | The cone of lower semicontinuous traces is studied with a view to its use as an invariant. Its properties include compactness, Hausdorffness, and continuity with respect to inductive limits. A suitable notion of dual cone is given. The cone of lower semicontinuous 2-quasitraces on a (non-exact) C*-algebra is considered as well. These results are applied to the study of the Cuntz semigroup. It is shown that if a C*-algebra absorbs the Jiang-Su algebra, then the subsemigroup of its Cuntz semigroup consisting of the purely non-compact elements is isomorphic to the dual cone of the cone of lower semicontinuous 2-quasitraces. This yields a computation of the Cuntz semigroup for the following two classes of C*-algebras: C*-algebras that absorb the Jiang-Su algebra and have no non-zero simple subquotients, and simple C*-algebras that absorb the Jiang-Su algebra. | |
| dc.identifier | https://arxiv.org/abs/0805.3122 | |
| dc.identifier | http://arxiv.org/abs/0805.3122 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/216558 | |
| dc.subject | Operator Algebras | |
| dc.title | The cone of lower semicontinuous traces on a C*-algebra | |
| dc.type | text |