# Decomposable Approximations Revisited

@article{Brown2016DecomposableAR,
title={Decomposable Approximations Revisited},
author={Nathanial P. Brown and Jos'e R. Carri'on and Stuart A. White},
journal={arXiv: Operator Algebras},
year={2016},
pages={45-59}
}
• Published 29 January 2016
• Mathematics
• arXiv: Operator Algebras
Nuclear C∗-algebras enjoy a number of approximation properties, most famously the completely positive approximation property. This was recently sharpened to arrange for the incoming maps to be sums of order-zero maps. We show that, in addition, the outgoing maps can be chosen to be asymptotically order-zero. Further these maps can be chosen to be asymptotically multiplicative if and only if the C∗-algebra and all its traces are quasidiagonal.
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Recently, it was proved by Tikuisis, White and Winter that any faithful trace on a separable, nuclear $C^\ast$-algebras in the UCT class is quasidiagonal. Building on their work, we generalise theExpand