Operator Algebra Seminar

Speaker: James Gabe (University of Copenhagen)

Title:Lifting theorems for completely positive maps

Abstract: Recall, that a completely positive map is nuclear if it is a point-norm limit of completely positive maps factoring through matrix algebras. The Choi-Effros lifting theorem says that any nuclear map from a separable C*-algebra A to a quotient C*-algebra lifts (to a nuclear map). We show that if A is exact then we may control this lift quite a bit. An application of this implies that ideal-related E-theory classifies all separable, nuclear, strongly purely infinite C*-algebras.