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Archiv der Mathematik

, Volume 90, Issue 6, pp 528–529 | Cite as

Order preserving transformations of the Hilbert grassmannian (note on the complex case)

  • Mark Pankov
Article

Abstract.

Let H be a separable complex Hilbert space and \({\mathcal{G}}_\infty (H)\) be the Grassmannian of closed subspaces with infinite dimension and codimension. We show that every order preserving bijective transformation of \({\mathcal{G}}_\infty (H)\) is induced by an invertible bounded semi-linear operator.

Mathematics Subject Classification (2000).

46C05 14M15 

Keywords.

Hilbert grassmannian order preserving transformation 

Copyright information

© Birkhaeuser 2008

Authors and Affiliations

  1. 1.Department of Mathematics and Information TechnologyUniversity of Warmia and MazuryOlsztynPoland

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