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arXiv · 1805.07937

Isometries of Grassmann spaces, II

Gy. P. Gehér·P. Šemrl
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Abstract

Botelho, Jamison, and Moln\'ar \cite{BJM}, and Geh\' er and \v{S}emrl \cite{GeS} have recently described the general form of surjective isometries of Grassmann spaces of all projections of a fixed finite rank on a Hilbert space $H$. As a straightforward consequence one can characterize surjective isometries of Grassmann spaces of projections of a fixed finite corank. In this paper we solve the remaining structural problem for surjective isometries on the set $P_\infty (H)$ of all projections of infinite rank and infinite corank when $H$ is separable. The proof technique is entirely different from the previous ones and is based on the study of geodesics in the Grassmannian $P_\infty (H)$. However, the same method gives an alternative proof in the case of finite rank projections.

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Gy. P. Gehér, P. Šemrl. 2018-05-21. Isometries of Grassmann spaces, II. https://arxiv.org/abs/1805.07937

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