Order preserving transformations of the Hilbert grassmannian: complex case
Functional Analysis
2007-05-23 v1 Operator Algebras
Abstract
Let be a separable complex Hilbert space. Denote by the Grassmannian consisting of closed linear subspaces with infinite dimension and codimension. This Grassmannian is partially ordered by the inclusion relation. We show that every continuous order preserving bijective transformation of is induced by an invertible bounded semi-linear operator.
Cite
@article{arxiv.0704.3022,
title = {Order preserving transformations of the Hilbert grassmannian: complex case},
author = {Mark Pankov},
journal= {arXiv preprint arXiv:0704.3022},
year = {2007}
}