1. 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 

2. CJM 2003 (vol 55 pp. 449)
 Albeverio, Sergio; Makarov, Konstantin A.; Motovilov, Alexander K.

Graph Subspaces and the Spectral Shift Function
We obtain a new representation for the solution to the operator
Sylvester equation in the form of a Stieltjes operator integral.
We also formulate new sufficient conditions for the strong
solvability of the operator Riccati equation that ensures the
existence of reducing graph subspaces for block operator matrices.
Next, we extend the concept of the LifshitsKrein spectral shift
function associated with a pair of selfadjoint operators to the
case of pairs of admissible operators that are similar to
selfadjoint operators. Based on this new concept we express the
spectral shift function arising in a perturbation problem for block
operator matrices in terms of the angular operators associated with
the corresponding perturbed and unperturbed eigenspaces.
Categories:47B44, 47A10, 47A20, 47A40 

3. CJM 1999 (vol 51 pp. 850)
 Muhly, Paul S.; Solel, Baruch

Tensor Algebras, Induced Representations, and the Wold Decomposition
Our objective in this sequel to \cite{MSp96a} is to develop extensions,
to representations of tensor algebras over $C^{*}$correspondences, of
two fundamental facts about isometries on Hilbert space: The Wold
decomposition theorem and Beurling's theorem, and to apply these to
the analysis of the invariant subspace structure of certain subalgebras
of CuntzKrieger algebras.
Keywords:tensor algebras, correspondence, induced representation, Wold decomposition, Beurling's theorem Categories:46L05, 46L40, 46L89, 47D15, 47D25, 46M10, 46M99, 47A20, 47A45, 47B35 
