Šemrl, Peter Orthogonality preserving transformations on the set of \(n\)-dimensional subspaces of a Hilbert space. (English) Zbl 1071.47038 Ill. J. Math. 48, No. 2, 567-573 (2004). The author describes the general form of all bijective transformations on the set of all \(n\)-dimensional subspaces (\(n\) being a fixed positive integer) of a real or complex infinite-dimensional Hilbert space which preserve the orthogonality in both directions. It turns out that every such transformation is induced by either a unitary or an antinuitary operator on the underlying Hilbert space. The result is a remarkable generalization of Uhlhorn’s well-known theorem (covering the case when \(n=1\)) that plays a rather important role in some parts of quantum mechanics. Reviewer: Lajos Molnár (Debrecen) Cited in 2 ReviewsCited in 26 Documents MSC: 47B49 Transformers, preservers (linear operators on spaces of linear operators) Keywords:nonlinear preservers; preserving orthogonality PDFBibTeX XMLCite \textit{P. Šemrl}, Ill. J. Math. 48, No. 2, 567--573 (2004; Zbl 1071.47038)