Extensions of pure states and projections of norm one (Q1300163)

The author shows that the extension property for pure states of a \(C^*\)-subalgebra \(B\) of a \(C^*\)-algebra \(A\) leads to the existence of a projection of norm one \(R: A\to B\) when \(B\) is liminal with Hausdorff primitive ideal space. He shows further that \(R\) is given by an ``Dixmier process''. Some applications are given for AF-algebras and Kumjian's ultraliminary \(C^*\)-algebras.