# Decomposable approximations revisited

Brown, N
Carrión, J
White, S

2016

## Journal:

Operator algebras and applications — The Abel Symposium 2015

## Last Updated:

2020-02-22T02:14:11.633+00:00

12

## DOI:

10.1007/978-3-319-39286-8_2

45-65

## abstract:

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.

1049969

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