1. CJM Online first
 Bosa, Joan; Petzka, Henning

Comparison Properties of the Cuntz semigroup and applications to C*algebras
We study comparison properties in the category $\mathrm{Cu}$ aiming to
lift results to the C*algebraic setting. We introduce a new
comparison property and relate it to both the CFP and $\omega$comparison.
We show differences of all properties by providing examples,
which suggest that the corona factorization for C*algebras might
allow for both finite and infinite projections. In addition,
we show that R{\o}rdam's simple, nuclear C*algebra with a finite
and an infinite projection does not have the CFP.
Keywords:classification of C*algebras, cuntz semigroup Categories:46L35, 06F05, 46L05, 19K14 

2. CJM Online first
 Ng, P. W.; Skoufranis, P.

Closed convex hulls of unitary orbits in certain simple real rank zero C$^*$algebras
In this paper, we characterize the closures of convex hulls of
unitary orbits of selfadjoint operators in unital, separable,
simple C$^*$algebras with nontrivial tracial simplex, real
rank zero, stable rank one, and strict comparison of projections
with respect to tracial states. In addition, an upper bound
for the number of unitary conjugates in a convex combination
needed to approximate a selfadjoint are obtained.
Keywords:convex hull of unitary orbits, real rank zero C*algebras simple, eigenvalue function, majorization Category:46L05 

3. CJM 2012 (vol 65 pp. 481)
4. CJM 2012 (vol 65 pp. 485)
 Bice, Tristan Matthew

Filters in C*Algebras
In this paper we analyze states on C*algebras and
their relationship to filterlike structures of projections and
positive elements in the unit ball. After developing the basic theory
we use this to investigate the KadisonSinger conjecture, proving its
equivalence to an apparently quite weak paving conjecture and the
existence of unique maximal centred extensions of projections coming
from ultrafilters on the natural numbers. We then prove that Reid's
positive answer to this for qpoints in fact also holds for rapid
ppoints, and that maximal centred filters are obtained in this case.
We then show that consistently such maximal centred filters do not
exist at all meaning that, for every pure state on the Calkin algebra,
there exists a pair of projections on which the state is 1, even
though the state is bounded strictly below 1 for projections below
this pair. Lastly we investigate towers, using cardinal invariant
equalities to construct towers on the natural numbers that do and do
not remain towers when canonically embedded into the Calkin algebra.
Finally we show that consistently all towers on the natural numbers
remain towers under this embedding.
Keywords:C*algebras, states, KadinsonSinger conjecture, ultrafilters, towers Categories:46L03, 03E35 

5. CJM 2001 (vol 53 pp. 631)
 Walters, Samuel G.

KTheory of NonCommutative Spheres Arising from the Fourier Automorphism
For a dense $G_\delta$ set of real parameters $\theta$ in $[0,1]$
(containing the rationals) it is shown that the group $K_0 (A_\theta
\rtimes_\sigma \mathbb{Z}_4)$ is isomorphic to $\mathbb{Z}^9$, where
$A_\theta$ is the rotation C*algebra generated by unitaries $U$, $V$
satisfying $VU = e^{2\pi i\theta} UV$ and $\sigma$ is the Fourier
automorphism of $A_\theta$ defined by $\sigma(U) = V$, $\sigma(V) =
U^{1}$. More precisely, an explicit basis for $K_0$ consisting of
nine canonical modules is given. (A slight generalization of this
result is also obtained for certain separable continuous fields of
unital C*algebras over $[0,1]$.) The Connes Chern character $\ch
\colon K_0 (A_\theta \rtimes_\sigma \mathbb{Z}_4) \to H^{\ev} (A_\theta
\rtimes_\sigma \mathbb{Z}_4)^*$ is shown to be injective for a dense
$G_\delta$ set of parameters $\theta$. The main computational tool in
this paper is a group homomorphism $\vtr \colon K_0 (A_\theta
\rtimes_\sigma \mathbb{Z}_4) \to \mathbb{R}^8 \times \mathbb{Z}$
obtained from the Connes Chern character by restricting the
functionals in its codomain to a certain ninedimensional subspace of
$H^{\ev} (A_\theta \rtimes_\sigma \mathbb{Z}_4)$. The range of $\vtr$
is fully determined for each $\theta$. (We conjecture that this
subspace is all of $H^{\ev}$.)
Keywords:C*algebras, Ktheory, automorphisms, rotation algebras, unbounded traces, Chern characters Categories:46L80, 46L40, 19K14 
