Decomposable approximations of nuclear C*-algebras

Details Decomposable approximations of nuclear C*-algebras Decomposable approximations of nuclear C*-algebras

2011-09-12

arxiv.org/abs/1109.2379v2

Adv. Math., 230 (2012), 1029-1039

Mathematics

Operator Algebras

Typos and and a few minor points corrected. Adv. Math., to appear

Scientific paper

10.1016/j.aim.2012.03.028

We show that nuclear C*-algebras have a refined version of the completely
positive approximation property, in which the maps that approximately factorize
through finite dimensional algebras are convex combinations of order zero maps.
We use this to show that a separable nuclear C*-algebra A which is closely
contained in a C*-algebra B embeds into B.

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