Lattices of Closed Subspaces
Mark Pankov · Cambridge University Press eBooks · 2020
We present two closely connected classical results: a description of isomorphisms between the lattices of closed subspaces of infinite-dimensional normed spaces and Kakutani--Mackey’s theorem which characterizes the orthomodular lattices of infinite-dimensional complex Hilbert spaces. The final part of the chapter concerns extensions of order preserving transformations of Hilbert Grassmannians to isomorphisms of the corresponding lattices.