Isometries of Grassmann spaces, II

2018/05/21 by Gehér, Gy. P., Šemrl, P. · 1 citation
#FOS: Mathematics #Functional Analysis (math.FA) #Primary: 47B49 #Secondary: 54E40

paper · doi:10.48550/arxiv.1805.07937

Abstract

Botelho, Jamison, and Molnár \citeBJM, and Geh' er and Šemrl \citeGeS 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_∞ (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_∞ (H). However, the same method gives an alternative proof in the case of finite rank projections.

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