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1. CMB 2013 (vol 57 pp. 463)
Constructive Proof of Carpenter's Theorem We give a constructive proof of Carpenter's Theorem due to Kadison.
Unlike the original proof our approach also yields the
real case of this theorem.
Keywords:diagonals of projections, the SchurHorn theorem, the Pythagorean theorem, the Carpenter theorem, spectral theory Categories:42C15, 47B15, 46C05 
2. CMB 2010 (vol 54 pp. 193)
Measurements and $G_\delta$Subsets of Domains
In this paper we study domains, Scott
domains, and the existence of measurements. We
use a space created by D.~K. Burke to show that
there is a Scott domain $P$ for which $\max(P)$ is
a $G_\delta$subset of $P$ and yet no measurement
$\mu$ on $P$ has $\ker(\mu) = \max(P)$. We also
correct a mistake in the literature asserting that
$[0, \omega_1)$ is a space of this type. We show
that if $P$ is a Scott domain and $X \subseteq
\max(P)$ is a $G_\delta$subset of $P$, then $X$
has a $G_\delta$diagonal and is weakly
developable. We show that if $X \subseteq
\max(P)$ is a $G_\delta$subset of $P$, where
$P$ is a domain but perhaps not a Scott domain,
then $X$ is domainrepresentable,
firstcountable, and is the union of dense,
completely metrizable subspaces. We also
show that there is a domain $P$ such that
$\max(P)$ is the usual space of countable
ordinals and is a $G_\delta$subset of $P$ in
the Scott topology. Finally we show that the
kernel of a measurement on a Scott domain can
consistently be a normal, separable,
nonmetrizable Moore space.
Keywords:domainrepresentable, Scottdomainrepresentable, measurement, Burke's space, developable spaces, weakly developable spaces, $G_\delta$diagonal, Äechcomplete space, Moore space, $\omega_1$, weakly developable space, sharp base, AFcomplete Categories:54D35, 54E30, 54E52, 54E99, 06B35, 06F99 
3. CMB 2004 (vol 47 pp. 615)
$C^*$Algebras and Factorization Through Diagonal Operators Let $\cal A$ be a $C^*$algebra and $E$ be a Banach space with
the RadonNikodym property. We prove that if $j$ is an embedding
of $E$ into an injective Banach space then for every absolutely
summing operator $T:\mathcal{A}\longrightarrow E$, the composition
$j \circ T$ factors through a diagonal operator from $l^{2}$ into
$l^{1}$. In particular, $T$ factors through a Banach space with
the Schur property. Similarly, we prove that for $2

4. CMB 2003 (vol 46 pp. 388)
Tracially Quasidiagonal Extensions It is known that a unital simple $C^*$algebra $A$ with tracial
topological rank zero has real rank zero. We show in this note that,
in general, there are unital $C^*$algebras with tracial topological
rank zero that have real rank other than zero.
Let $0\to J\to E\to A\to 0$ be a short exact sequence of
$C^*$algebras. Suppose that $J$ and $A$ have tracial topological
rank zero. It is known that $E$ has tracial topological rank zero
as a $C^*$algebra if and only if $E$ is tracially quasidiagonal
as an extension. We present an example of a tracially
quasidiagonal extension which is not quasidiagonal.
Keywords:tracially quasidiagonal extensions, tracial rank Categories:46L05, 46L80 