Search: MSC category 46L45 ( Decomposition theory for $C^$-algebras *$-algebras * )  Expand all Collapse all Results 1 - 3 of 3 1. CJM Online first Kaftal, Victor; Ng, Ping Wong; Zhang, Shuang  Strict comparison of positive elements in multiplier algebras Main result: If a C*-algebra$\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$-unital C*-algebra can be approximated by a bi-diagonal series. An application of strict comparison: If$\mathcal{A}$is a simple separable stable C*-algebra with real rank zero, stable rank one, and strict comparison of positive elements by traces, then whether a positive element is a positive linear combination of projections is determined by the trace values of its range projection. Keywords:strict comparison, bi-diagonal form, positive combinationsCategories:46L05, 46L35, 46L45, 47C15 2. CJM 2003 (vol 55 pp. 1302) Katsura, Takeshi  The Ideal Structures of Crossed Products of Cuntz Algebras by Quasi-Free Actions of Abelian Groups We completely determine the ideal structures of the crossed products of Cuntz algebras by quasi-free actions of abelian groups and give another proof of A.~Kishimoto's result on the simplicity of such crossed products. We also give a necessary and sufficient condition that our algebras become primitive, and compute the Connes spectra and$K$-groups of our algebras. Categories:46L05, 46L55, 46L45 3. CJM 1998 (vol 50 pp. 323) Dykema, Kenneth J.; Rørdam, Mikael  Purely infinite, simple$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$-algebras by any of a certain class of non-unital endomorphisms; \item{(3)} those that arise as reduced free products of pairs of$C^\ast\$-algebras with respect to any from a certain class of states. Categories:46L05, 46L45