Extensions by simple $C^*$algebras  Quasidiagonal extensions
Abstract
Let $A$ be an amenable separable \CA and $B$ be a nonunital but $\sigma$unital simple \CA with continuous scale. We show that two essential extensions $\tau_1$ and $\tau_2$ of $A$ by $B$ are approximately unitarily equivalent if and only if $$ [\tau_1]=[\tau_2] {\rm in} KL(A, M(B)/B). $$ 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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 January 2004
 arXiv:
 arXiv:math/0401241
 Bibcode:
 2004math......1241L
 Keywords:

 Operator Algebras;
 46L05;
 46L35
 EPrint:
 to appear Canad J. Math