A simple characterization of Aerts's separated product
Boris Ischi · arXiv (Cornell University) · 2004
Abstract. Let H1 and H2 be complex Hilbert spaces, L1 = P(H1) and L2 = P(H2) the lattices of closed subspaces, and let L be a complete atomistic lattice. We prove under some weak assumptions relating Li and L, that if L admits an orthocomplementation, then L is isomorphic to the separated product of L1 and L2 defined by Aerts. The proof does not require any assumption on the orthocomplementation of L. 1.