#### Vol. 4, No. 1, 2006

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Base subsets of the Hilbert Grassmannian

### Mark Pankov

Vol. 4 (2006), No. 1, 63–68
##### Abstract

Let $H$ be a separable Hilbert space. We consider the Hilbert Grassmannian ${\mathsc{G}}_{\infty }\left(H\right)$ consisting of closed subspaces having infinite dimension and codimension and show that every bijective transformation of ${\mathsc{G}}_{\infty }\left(H\right)$ preserving the class of base subsets is induced by an element of $GL\left(H\right)$ or it is the composition of the transformation induced by an element of $GL\left(H\right)$ and the bijection sending a subspace to its orthogonal complement.

##### Keywords
Hilbert Grassmannian, base subset, infinite-dimensional topological projective space
##### Mathematical Subject Classification 2000
Primary: 46C05, 51E24