User:Hannes.thiel/Choi–Effros lifting theorem

Choi-Effros lifting theorem

In mathematics, especially functional analysis, the Choi-Effros lifting theorem states that a nuclear *-homomorphism from a separable C*-algebra A to a quotient C*-algebra B/J has a completely positive lift $$A\mapsto B$$. In particular, every *-homomorphism from a separable, nuclear C*-algebra to a quotient C*-algebra has a completely positive lift. This result was proven by Man-Duen Choi and Edward Effros in 1976 and was a significant point in the development of the structure theory of C*-algebras.