Quantum logic, state space geometry and operator algebras (Q1071766)

This short paper concerns the geometric characterization of a particular class of \(\sigma\)-complete orthomodular lattices, in particular of the lattice of projections of a von Neumann algebra and the lattice of projections in certain Jordan operator algebras known as JBW-algebras. The authors perhaps advance a short step closer towards a characterization of these lattices, by finding three geometric properties which do characterize a subclass of them. This is the subclass satisfying the countable chain condition, and satisfying another more complex condition which ensures they are not too ''pathologically'' non-classical. This paper will interest those concerned with the geometric characterization of orthomodular lattices. There is no discussion of implications to quantum theory.