The Completely Positive Lifting Problem for C ∗ -algebras

Abstract

(1.1)~~~~~~~~~~~~~~~~~~~1 where A, B are C*-algebras (resp., unital C*-algebras), J is a closed twosided ideal in B, 7 is the quotient map, and A, * are contractive (resp., unital) completely positive maps. The lifting problem for q is to determine whether or not one can find * so that the diagram commutes. In this paper, we will show that this is the case if A is separable, and either A, B/J, or B