Illinois Journal of Mathematics
- Illinois J. Math.
- Volume 48, Number 2 (2004), 567-573.
Orthogonality preserving transformations on the set of $n$-dimensional subspaces of a Hilbert space
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
