1. CJM 2007 (vol 59 pp. 343)
 Lin, Huaxin

Weak Semiprojectivity in Purely Infinite Simple $C^*$Algebras
Let $A$ be a separable amenable purely infinite simple \CA which
satisfies the Universal Coefficient Theorem. We prove that $A$ is
weakly semiprojective if and only if $K_i(A)$ is a countable
direct sum of finitely generated groups ($i=0,1$). Therefore, if
$A$ is such a \CA, for any $\ep>0$ and any finite subset ${\mathcal
F}\subset A$ there exist $\dt>0$ and a finite subset ${\mathcal
G}\subset A$ satisfying the following: for any contractive
positive linear map $L: A\to B$ (for any \CA $B$) with $
\L(ab)L(a)L(b)\<\dt$ for $a, b\in {\mathcal G}$
there exists a homomorphism $h\from A\to B$ such that
$ \h(a)L(a)\<\ep$ for $a\in {\mathcal F}$.
Keywords:weakly semiprojective, purely infinite simple $C^*$algebras Categories:46L05, 46L80 

2. CJM 2005 (vol 57 pp. 351)
 Lin, Huaxin

Extensions by Simple $C^*$Algebras: Quasidiagonal Extensions
Let $A$ be an amenable separable $C^*$algebra and $B$ be a nonunital
but $\sigma$unital simple $C^*$algebra 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
$$
[\tau_1]=[\tau_2] \text{ in } KL(A, M(B)/B).
$$
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.
Keywords:Extensions, Simple $C^*$algebras Categories:46L05, 46L35 
