1. CMB 2016 (vol 59 pp. 564)
 Li, Boyu

Normal Extensions of Representations of Abelian Semigroups
A commuting family of subnormal operators need
not have a commuting normal extension. We study when a representation
on an abelian semigroup can be extended to a normal representation,
and show that it suffices to extend the set of generators to
commuting normals. We also extend a result due to Athavale to
representations on abelian lattice ordered semigroups.
Keywords:subnormal operator, normal extension, regular dilation, lattice ordered semigroup Categories:47B20, 47A20, 47D03 

2. CMB 2014 (vol 58 pp. 9)
 Chavan, Sameer

Irreducible Tuples Without the Boundary Property
We examine spectral behavior of irreducible tuples which do not
admit boundary property. In particular, we prove under some mild
assumption that the spectral radius of such an $m$tuple $(T_1,
\dots, T_m)$ must be the operator norm of $T^*_1T_1 + \cdots +
T^*_mT_m$. We use this simple observation to ensure boundary
property for an irreducible, essentially normal joint $q$isometry provided it
is not a joint isometry.
We further exhibit a family of
reproducing Hilbert $\mathbb{C}[z_1, \dots, z_m]$modules (of which
the DruryArveson Hilbert module is a prototype) with the property that any
two nested unitarily equivalent submodules are indeed equal.
Keywords:boundary representations, subnormal, joint pisometry Categories:47A13, 46E22 

3. CMB 2011 (vol 56 pp. 459)
 Athavale, Ameer; Patil, Pramod

On Certain Multivariable Subnormal Weighted Shifts and their Duals
To every subnormal $m$variable weighted shift $S$ (with bounded
positive weights) corresponds a positive Reinhardt measure $\mu$
supported on a compact Reinhardt subset of $\mathbb C^m$. We show that, for
$m \geq 2$, the dimensions of the $1$st cohomology vector spaces
associated with the Koszul complexes of $S$ and its dual ${\tilde S}$
are different if a certain radial function happens to be integrable
with respect to $\mu$ (which is indeed the case with many classical
examples). In particular, $S$ cannot in that case be similar to
${\tilde S}$. We next prove that, for $m \geq 2$, a Fredholm subnormal
$m$variable weighted shift $S$ cannot be similar to its dual.
Keywords:subnormal, Reinhardt, Betti numbers Category:47B20 
