Representations of MV-Algebras by Hilbert-Space Effects

It is shown that for every Archimedean MV-effect algebra M (equivalently, every Archimedean MV-algebra) there is an injective MV-algebra morphism into the MV-algebra of all multiplication operators between the zero and identity operator on $ell_{2}(mathcal{S}_{0})$ , where $mathcal{S}_{0}$ is an ordering set of extremal states (state morphisms) on M.