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

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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.

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  1. Department of Mathematics and Information Technology, University of Warmia and Mazury, Żolnierska 14A, 10-561, Olsztyn, Poland

    Mark Pankov

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  1. Mark Pankov
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Correspondence to Mark Pankov.

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Received: 23 October 2007

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Pankov, M. Order preserving transformations of the Hilbert grassmannian (note on the complex case). Arch. Math. 90, 528–529 (2008). https://doi.org/10.1007/s00013-008-2416-3

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  • DOI: https://doi.org/10.1007/s00013-008-2416-3

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