1. CMB 2014 (vol 58 pp. 91)
 Hasegawa, Kei

Essential Commutants of Semicrossed Products
Let $\alpha\colon G\curvearrowright M$ be a spatial action of countable
abelian group on a "spatial" von Neumann algebra $M$ and $S$ be its
unital subsemigroup with $G=S^{1}S$. We explicitly compute the
essential commutant and the essential fixedpoints, modulo the
Schatten $p$class or the compact operators, of the w$^*$semicrossed
product of $M$ by $S$ when $M'$ contains no nonzero compact
operators. We also prove a weaker result when $M$ is a von Neumann
algebra on a finite dimensional Hilbert space and
$(G,S)=(\mathbb{Z},\mathbb{Z}_+)$, which extends a famous result due
to Davidson (1977) for the classical analytic Toeplitz operators.
Keywords:essential commutant, semicrossed product Categories:47L65, 47A55 

2. CMB 2012 (vol 57 pp. 80)
 Khemphet, Anchalee; Peters, Justin R.

Semicrossed Products of the Disk Algebra and the Jacobson Radical
We consider semicrossed products of the disk algebra with respect to
endomorphisms defined by finite Blaschke products. We characterize the Jacobson radical
of these operator algebras. Furthermore, in the case the finite Blaschke product is elliptic,
we show that the semicrossed product contains no nonzero quasinilpotent
elements. However, if the finite Blaschke product is hyperbolic or parabolic with positive hyperbolic step,
the Jacobson radical is nonzero and a proper subset of the set of quasinilpotent elements.
Keywords:semicrossed product, disk algebra, Jacobson radical Categories:47L65, 47L20, 30J10, 30H50 
