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- W2953353614 abstract "Let $H$ be a separable real Hilbert space. Denote by ${mathcal G}_{infty}(H)$ the Grassmannian consisting of closed subspaces with infinite dimension and codimension. This Grassmannian is partially ordered by the inclusion relation. We show that every order preserving transformation of ${mathcal G}_{infty}(H)$ can be extended to an automorphism of the lattice of closed subspaces of $H$. It follows from Mackey's result cite{Mackey} that automorphisms of this lattice are induced by invertible bounded linear operators." @default.
- W2953353614 created "2019-06-27" @default.
- W2953353614 creator A5060769535 @default.
- W2953353614 date "2006-05-14" @default.
- W2953353614 modified "2023-09-23" @default.
- W2953353614 title "Order preserving transformations of the Hilbert grassmannian" @default.
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