Enlargements of quantum logics (Q1821801)

Let K be a quantum logic whose state space is nonvoid. Let B be a Boolean algebra and let C be a compact convex subset of a locally convex topological linear space. Then K can be embedded into a logic L such that the centre of L equals B and the state space of L equals C. (The result remains valid when we replace the word ''logic'' with ''orthomodular lattice''.)