1. CMB Online first
 Lin, Minghua

A determinantal inequality involving partial traces
Let $\mathbf{A}$ be a density matrix in $\mathbb{M}_m\otimes
\mathbb{M}_n$. Audenaert [J. Math. Phys. 48 (2007) 083507] proved
an inequality for Schatten $p$norms:
\[
1+\\mathbf{A}\_p\ge \\tr_1 \mathbf{A}\_p+\\tr_2 \mathbf{A}\_p,
\]
where $\tr_1, \tr_2$ stand for the first and second partial
trace, respectively. As an analogue of his result, we prove a
determinantal inequality
\[
1+\det \mathbf{A}\ge \det(\tr_1 \mathbf{A})^m+\det(\tr_2 \mathbf{A})^n.
\]
Keywords:determinantal inequality, partial trace, block matrix Categories:47B65, 15A45, 15A60 

2. CMB 1998 (vol 41 pp. 298)
 Jahandideh, M. T.

On the idealtriangularizability of semigroups of quasinilpotent positive operators on $C({\cal K})$
It is known that a semigroup of quasinilpotent integral operators,
with positive lower semicontinuous kernels, on $L^2( X, \mu)$,
where $X$ is a locally compact HausdorffLindel\"of space and $\mu$
is a $\sigma$finite regular Borel measure on $X$, is
triangularizable. In this article we use the Banach lattice version
of triangularizability to establish the idealtriangularizability
of a semigroup of positive quasinilpotent integral operators on
$C({\cal K})$ where ${\cal K}$ is a compact Hausdorff space.
Category:47B65 
