Abstract
In answer to open questions (posed in [ 12 ]) we prove that an effect algebra has a Hilbert space effect-representation iff E possesses an ordering set of states. These are, up to isomorphism, all intervals and all their sub-effect algebras in the set of all positive linear operators on any Hilbert space H . Nevertheless, there are effect algebras E , elements of which are linear operators in a Hilbert space, but E does not have such a representation.
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