An extended characterisation theorem for quantum logics

Two theorems are proved. In the first properties of an important mapping from an orthocomplemented lattice to itself are studied. In the second the authors extend the characterisation theorem of Zierler (1961) to get a very useful theorem characterising orthomodular lattices Since quantum logics are merely sigma -complete orthomodular lattices, the principal result is, for application in quantum physics, a characterisation theorem for quantum logics.