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Maps on the $ n$-dimensional subspaces of a Hilbert space preserving principal angles


Author: Lajos Molnár
Journal: Proc. Amer. Math. Soc. 136 (2008), 3205-3209
MSC (2000): Primary 47B49, 15A30
DOI: https://doi.org/10.1090/S0002-9939-08-09317-9
Published electronically: April 29, 2008
MathSciNet review: 2407085
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Abstract: In a former paper we studied transformations on the set of all $ n$-dimensional subspaces of a Hilbert space $ H$ which preserve the principal angles. In the case when $ \dim H\neq 2n$, we could determine the general form of all such maps. The aim of this paper is to complete our result by considering the problem in the remaining case $ \dim H=2n$.


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Additional Information

Lajos Molnár
Affiliation: Institute of Mathematics, P.O. Box 12, University of Debrecen, H-4010 Debrecen, Hungary
Email: molnarl@math.klte.hu

DOI: https://doi.org/10.1090/S0002-9939-08-09317-9
Keywords: Wigner's theorem, projections, subspaces, principal angles, preservers
Received by editor(s): March 28, 2007
Received by editor(s) in revised form: July 18, 2007
Published electronically: April 29, 2008
Additional Notes: The author was supported by the Hungarian National Foundation for Scientific Research (OTKA), Grant No. T046203, NK68040.
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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