Extensions by simple $C^*$-algebras -- Quasidiagonal extensions
| dc.creator | Lin, Huaxin | |
| dc.date | 2004-01-19 | |
| dc.date.accessioned | 2026-07-07T05:04:40Z | |
| dc.date.available | 2026-07-07T05:04:40Z | |
| dc.description | Let $A$ be an amenable separable \CA and $B$ be a non-unital but $σ$-unital simple \CA with continuous scale. We show that two essential extensions $τ_1$ and $τ_2$ of $A$ by $B$ are approximately unitarily equivalent if and only if $$ [τ_1]=[τ_2] {\rm in} KL(A, M(B)/B). $$ If $A$ is assumed to satisfy the Universal Coefficient Theorem, there is a bijection from approximate unitary equivalence classes of the above mentioned extensions to $KL(A, M(B)/B).$ Using $KL(A, M(B)/B),$ we compute exactly when an essential extension is quasidiagonal. We show that quasidiagonal extensions may not be approximately trivial. We also study the approximately trivial extensions. | |
| dc.description | to appear Canad J. Math | |
| dc.identifier | https://arxiv.org/abs/math/0401241 | |
| dc.identifier | http://arxiv.org/abs/math/0401241 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69897 | |
| dc.subject | Operator Algebras | |
| dc.subject | 46L05; 46L35 | |
| dc.title | Extensions by simple $C^*$-algebras -- Quasidiagonal extensions | |
| dc.type | text |