Olson Order of Quantum Observables

Using ideas of Olson \cite{Ols} who showed that the system of effect operators of a Hilbert space can be ordered by the so-called spectral order such that the system of effect operators is a complete lattice. Using his ideas, we introduce a partial order, called the Olson order, on the set of bounded observables of a complete lattice effect algebra. We show that the set of bounded observables is a Dedekind complete lattice.0