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Maps on the  -dimensional subspaces of a Hilbert space preserving principal angles
Author(s):
Lajos
Molnár
Journal:
Proc. Amer. Math. Soc.
136
(2008),
3205-3209.
MSC (2000):
Primary 47B49, 15A30
Posted:
April 29, 2008
MathSciNet review:
2407085
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Abstract:
In a former paper we studied transformations on the set of all  -dimensional subspaces of a Hilbert space  which preserve the principal angles. In the case when  , 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  .
References:
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- 2.
- M.D. Choi, A.A. Jafarian and H. Radjavi, Linear maps preserving commutativity, Linear Algebra Appl. 87 (1987), 227-241. MR 878680 (88f:15003)
- 3.
- H. Hotelling, Relations between two sets of variates, Biometrika 28 (1935), 321-377.
- 4.
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 dimensions, Bull. Soc. Math. France 3 (1875), 103-174. MR 1503705 - 5.
- L. Molnár, Transformations on the set of all
 -dimensional subspaces of a Hilbert space preserving principal angles, Commun. Math. Phys. 217 (2001), 409-421. MR 1821230 (2002b:81008) - 6.
- L. Molnár, Selected Preserver Problems on Algebraic Structures of Linear Operators and on Function Spaces, Lecture Notes in Mathematics, Vol. 1895, Springer, 2006. MR 2267033 (2007g:47056)
- 7.
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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:
10.1090/S0002-9939-08-09317-9
PII:
S 0002-9939(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
Posted:
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
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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