Projection lattices in a Hilbert space
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.
limits in the Hausdorff sense, corresponding to the uw topology for the algebras and the strong operator topology for the lattices
scientific article; zbMATH DE number 4163588