Order preserving transformations of the Hilbert grassmannian
| dc.creator | Pankov, Mark | |
| dc.date | 2006-05-14 | |
| dc.date.accessioned | 2026-07-07T07:14:12Z | |
| dc.date.available | 2026-07-07T07:14:12Z | |
| dc.description | 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. | |
| dc.identifier | https://arxiv.org/abs/math/0605363 | |
| dc.identifier | http://arxiv.org/abs/math/0605363 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/112778 | |
| dc.subject | Functional Analysis | |
| dc.subject | Combinatorics | |
| dc.title | Order preserving transformations of the Hilbert grassmannian | |
| dc.type | text |