3 - Lattices of Closed Subspaces
Published online by Cambridge University Press: 06 January 2020
Summary
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.
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- Information
- Wigner-Type Theorems for Hilbert Grassmannians , pp. 53 - 67Publisher: Cambridge University PressPrint publication year: 2020