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Search: MSC category 47B65 ( Positive operators and order-bounded operators )

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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 ideal-triangularizability 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 Hausdorff-Lindel\"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 ideal-triangularizability of a semigroup of positive quasinilpotent integral operators on $C({\cal K})$ where ${\cal K}$ is a compact Hausdorff space.

Category:47B65

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