1. CJM 2013 (vol 67 pp. 132)
 Clouâtre, Raphaël

Unitary Equivalence and Similarity to Jordan Models for Weak Contractions of Class $C_0$
We obtain results on the unitary equivalence of weak contractions of
class $C_0$ to their Jordan models under an assumption on their
commutants. In particular, our work addresses the case of arbitrary
finite multiplicity. The main tool is the
theory of boundary representations due to Arveson. We also
generalize and improve previously known results concerning unitary
equivalence and similarity to Jordan models when the minimal function
is a Blaschke product.
Keywords:weak contractions, operators of class $C_0$, Jordan model, unitary equivalence Categories:47A45, 47L55 

2. CJM 2012 (vol 65 pp. 768)
 Fuller, Adam Hanley

Nonselfadjoint Semicrossed Products by Abelian Semigroups
Let $\mathcal{S}$ be the semigroup $\mathcal{S}=\sum^{\oplus k}_{i=1}\mathcal{S}_i$, where for each $i\in I$,
$\mathcal{S}_i$ is a countable subsemigroup of the additive semigroup $\mathbb{R}_+$ containing $0$. We consider representations
of $\mathcal{S}$ as contractions $\{T_s\}_{s\in\mathcal{S}}$ on a Hilbert space with the Nicacovariance property:
$T_s^*T_t=T_tT_s^*$ whenever $t\wedge s=0$. We show that all such representations have a unique minimal isometric Nicacovariant
dilation.
This result is used to help analyse the nonselfadjoint semicrossed product algebras formed from Nicacovariant representations of the action of $\mathcal{S}$ on an operator algebra $\mathcal{A}$ by completely contractive endomorphisms.
We conclude by calculating the $C^*$envelope of the isometric nonselfadjoint semicrossed product algebra (in the sense
of Kakariadis and Katsoulis).
Keywords:semicrossed product, crossed product, C*envelope, dilations Categories:47L55, 47A20, 47L65 

3. CJM 2009 (vol 61 pp. 1239)
 Davidson, Kenneth R.; Yang, Dilian

Periodicity in Rank 2 Graph Algebras
Kumjian and Pask introduced an aperiodicity condition
for higher rank graphs.
We present a detailed analysis of when this occurs
in certain rank 2 graphs.
When the algebra is aperiodic, we give another proof
of the simplicity of $\mathrm{C}^*(\mathbb{F}^+_{\theta})$.
The periodic $\mathrm{C}^*$algebras are characterized, and it is shown
that $\mathrm{C}^*(\mathbb{F}^+_{\theta}) \simeq
\mathrm{C}(\mathbb{T})\otimes\mathfrak{A}$
where $\mathfrak{A}$ is a simple $\mathrm{C}^*$algebra.
Keywords:higher rank graph, aperiodicity condition, simple $\mathrm{C}^*$algebra, expectation Categories:47L55, 47L30, 47L75, 46L05 
