The Fine Structure of the Kasparov Groups III: Relative Quasidiagonality
| dc.creator | Schochet, Claude | |
| dc.date | 2001-07-12 | |
| dc.date.accessioned | 2026-07-07T04:42:34Z | |
| dc.date.available | 2026-07-07T04:42:34Z | |
| dc.description | In this paper we identify QD(A,B), the quasidiagonal classes in KK_1(A,B), in terms of K_*(A) and K_*(B), and we use these results in various applications. Here is our central result. Theorem: Suppose that A is in the category of separable nuclear C^*-algebras which satisfy the UCT and A is quasidiagonal relative to B. Then there is a natural isomorphism QD(A,B) = Pext (K_*(A), K_*(B))_0 . Thus quasidiagonality of KK-classes is indeed a topological invariant. We give several applications. Finally, we establish a converse to a theorem of Davidson, Herrero, and Salinas, giving conditions under which the quasidiagonality of A/K implies the quasidiagonality of the associated representation of A. | |
| dc.description | 34 pages | |
| dc.identifier | https://arxiv.org/abs/math/0107090 | |
| dc.identifier | http://arxiv.org/abs/math/0107090 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/61839 | |
| dc.subject | Operator Algebras | |
| dc.subject | Functional Analysis | |
| dc.subject | 46L80, 47A66, 19K35 (Primary) | |
| dc.title | The Fine Structure of the Kasparov Groups III: Relative Quasidiagonality | |
| dc.type | text |