Nuclear C*-algebra

Characterizations

• The identity map, as a completely positive map, approximately factors through matrix algebras. By this equivalence, nuclearity can be considered a noncommutative analogue of the existence of partitions of unity.
• The enveloping von Neumann algebra is injective.
• It is amenable as a Banach algebra.
• It is isomorphic to a C*-subalgebra B of the Cuntz algebra with the property that there exists a conditional expectation from to B. This condition is only equivalent to the others for separable C*-algebras.