On Realization of Generalized Effect Algebras

A well-known fact is that there is a finite orthomodular lattice with an order determining set of states which is not representable in the standard quantum logic, the lattice L ( H ) of all closed subspaces of a separable complex Hilbert space. w that a generalized effect algebra is representable in the operator generalized effect algebra G D ( H ) of effects of a complex Hilbert space H iff it has an order determining set of generalized states. This extends the corresponding results for effect algebras of Riečanová and Zajac. Further, any operator generalized effect algebra G D ( H ) possesses an order determining set of generalized states.