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Isometries of Grassmann spaces, II

Geher, G. P. and Semrl, P. (2018) Isometries of Grassmann spaces, II. Advances in Mathematics, 332 (9). pp. 287-310. ISSN 1090-2082

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To link to this item DOI: 10.1016/j.aim.2018.05.012

Abstract/Summary

Botelho, Jamison, and Molnár [1], and Gehér and Šemrl [4] 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 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 . However, the same method gives an alternative proof in the case of finite rank projections.

Item Type:Article
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:77194
Publisher:Elsevier

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