Foundations of Physics 41 (10):1634-1647 (2011)

Abstract
We show that considerable sets of positive linear operators namely their extensions as closures, adjoints or Friedrichs positive self-adjoint extensions form operator (generalized) effect algebras. Moreover, in these cases the partial effect algebraic operation of two operators coincides with usual sum of operators in complex Hilbert spaces whenever it is defined. These sets include also unbounded operators which play important role of observables (e.g., momentum and position) in the mathematical formulation of quantum mechanics
Keywords Quantum structures  (Generalized) effect algebra  Hilbert space  (Unbounded) positive linear operator  Closure  Adjoint  Friedrichs extension
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DOI 10.1007/s10701-011-9573-0
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References found in this work BETA

Effect Algebras and Unsharp Quantum Logics.D. J. Foulis & M. K. Bennett - 1994 - Foundations of Physics 24 (10):1331-1352.
Effects, Observables, States, and Symmetries in Physics.David J. Foulis - 2007 - Foundations of Physics 37 (10):1421-1446.

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