Decomposable approximations revisited
Operator Algebras
2017-08-25 v4
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.
Keywords
Cite
@article{arxiv.1602.00021,
title = {Decomposable approximations revisited},
author = {Nathanial P. Brown and José R. Carrión and Stuart White},
journal= {arXiv preprint arXiv:1602.00021},
year = {2017}
}
Comments
New section 4 added, providing a lifting lemma needed for the statement of Prop 3.2. Footnote 5 added to end of proof of Prop 3.2, and bibliography and precise locations of references updated. No other changes made to sects 1-3. 19 Pages