Decomposition of Projections on Orthomodular Lattices(1)
Gottfried T. Rüttimann · Canadian Mathematical Bulletin · 1975
The set of projections in the BAER*-semigroup of hemimorphisms on an orthomodular latticeLcan be partially ordered such that the subset of closed projections becomes an orthocomplemented lattice isomorphic to the underlying latticeL. The set of closed projections is identical with the set of Sasaki-projections onL(Foulis [2]). Another interesting class of (in general nonclosed) projections, first investigated by Janowitz [4], are the symmetric closure operators. They map onto orthomodular sublattices where Sasaki-projections map onto segments of the latticeL.