Abstract
The following result is proved: letE be anF-space (that is, the space of all continuous affine functions defined on a compact universal cap van shing at zero) and letMχE be anM-ideal. Then, ifE/M is a π1 with positive defining projections, then there is a positive linear operator ϱ:E/M→E of norm one such that ϱ lifts the canonical mapE→E/M. In the proof, which heavily depends on work of Ando, we study ensor products of certain convex cones with compact bases, and we calculate the norm of a positive linear operator defined on a finite dimensional space with range in aF-space. Various corollaries are deduced for split faces of compact convex sets and for morphisms ofC*-algebras.
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