Vol. 4, No. 1, 2006

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Base subsets of the Hilbert Grassmannian

Mark Pankov

Vol. 4 (2006), No. 1, 63–68

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

Hilbert Grassmannian, base subset, infinite-dimensional topological projective space
Mathematical Subject Classification 2000
Primary: 46C05, 51E24
Received: 8 May 2006
Accepted: 27 December 2006
Mark Pankov