Decomposable approximations revisited

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.

arXiv commentNew 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

References in corpus (8)

• Completely positive maps of order zero
• Nuclear dimension and Z-stability
• Invariant means and finite representation theory of C*-algebras
• Decomposable approximations of nuclear C*-algebras
• Nuclear dimension and n-comparison
• Quasitraces are Traces: A Short Proof of the Finite-Nuclear-Dimension Case
• Quasidiagonal traces on exact $C^{\ast }$-algebras
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Cited by in corpus (2)

• Nuclear dimension of simple C*-algebras
• Nuclear dimension of simple stably projectionless C*-algebras