1. CJM 2016 (vol 69 pp. 373)
 Kaftal, Victor; Ng, Ping Wong; Zhang, Shuang

Strict Comparison of Positive Elements in Multiplier Algebras
Main result: If a C*algebra $\mathcal{A}$ is simple, $\sigma$unital,
has finitely many extremal traces, and has strict comparison
of positive elements by traces, then its multiplier algebra
$\operatorname{\mathcal{M}}(\mathcal{A})$
also has strict comparison of positive elements by traces. The
same results holds if ``finitely many extremal traces" is replaced
by ``quasicontinuous scale".
A key ingredient in the proof is that every positive element
in the multiplier algebra of an arbitrary $\sigma$unital C*algebra
can be approximated by a bidiagonal series.
An application of strict comparison: If $\mathcal{A}$ is a simple separable
stable C*algebra with real rank zero, stable rank one, and
strict comparison of positive elements by traces, then whether
a positive element is a positive linear combination of projections
is determined by the trace values of its range projection.
Keywords:strict comparison, bidiagonal form, positive combinations Categories:46L05, 46L35, 46L45, 47C15 

2. CJM 2003 (vol 55 pp. 1302)
3. CJM 1998 (vol 50 pp. 323)
 Dykema, Kenneth J.; Rørdam, Mikael

Purely infinite, simple $C^\ast$algebras arising from free product constructions
Examples of simple, separable, unital, purely infinite
$C^\ast$algebras are constructed, including:
\item{(1)} some that are not approximately divisible;
\item{(2)} those that arise as crossed products of any of a certain class of
$C^\ast$algebras by any of a certain class of nonunital endomorphisms;
\item{(3)} those that arise as reduced free products of pairs of
$C^\ast$algebras with respect to any from a certain class of states.
Categories:46L05, 46L45 
