Projection lattices in a Hilbert space (Q920380)

The continuity of the mapping \({\mathcal A}\to Lat {\mathcal A}\) is investigated for subalgebras of a von Neumann algebra. The algebras are supposed closed in the ultraweak topology, Lat \({\mathcal A}\) is identified with the lattices of the corresponding projections. Main result: If lim \({\mathcal A}_ n={\mathcal A}\) then lim Lat \({\mathcal A}_ n=Lat {\mathcal A}\). The limits in the Hausdorff sense, corresponding to the uw topology for the algebras and the strong operator topology for the lattices.