Illinois Journal of Mathematics

Orthogonality preserving transformations on the set of $n$-dimensional subspaces of a Hilbert space

Peter Šemrl

Full-text: Open access

Abstract

We characterize bijective transformations on the set of all $n$-dimensional subspaces of a Hilbert space that preserve orthogonality in both directions. This extends Uhlhorn's improvement of Wigner's classical theorem on symmetry transformations.

Article information

Source
Illinois J. Math., Volume 48, Number 2 (2004), 567-573.

Dates
First available in Project Euclid: 13 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258138399

Digital Object Identifier
doi:10.1215/ijm/1258138399

Mathematical Reviews number (MathSciNet)
MR2085427

Zentralblatt MATH identifier
1071.47038

Subjects
Primary: 47B49: Transformers, preservers (operators on spaces of operators)
Secondary: 47N50: Applications in the physical sciences

Citation

Šemrl, Peter. Orthogonality preserving transformations on the set of $n$-dimensional subspaces of a Hilbert space. Illinois J. Math. 48 (2004), no. 2, 567--573. doi:10.1215/ijm/1258138399. https://projecteuclid.org/euclid.ijm/1258138399


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