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

Molnár, Lajos

doi:10.1090/S0002-9939-08-09317-9

Maps on the $n$-dimensional subspaces of a Hilbert space preserving principal angles
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Proc. Amer. Math. Soc. 136 (2008), 3205-3209 Request permission

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 $\dim H=2n$.

References

Rajendra Bhatia, Matrix analysis, Graduate Texts in Mathematics, vol. 169, Springer-Verlag, New York, 1997. MR 1477662, DOI 10.1007/978-1-4612-0653-8
M. D. Choi, A. A. Jafarian, and H. Radjavi, Linear maps preserving commutativity, Linear Algebra Appl. 87 (1987), 227–241. MR 878680, DOI 10.1016/0024-3795(87)90169-8
H. Hotelling, Relations between two sets of variates, Biometrika 28 (1935), 321-377.
Camille Jordan, Essai sur la géométrie à $n$ dimensions, Bull. Soc. Math. France 3 (1875), 103–174 (French). MR 1503705, DOI 10.24033/bsmf.90
Lajos Molnár, Transformations on the set of all $n$-dimensional subspaces of a Hilbert space preserving principal angles, Comm. Math. Phys. 217 (2001), no. 2, 409–421. MR 1821230, DOI 10.1007/PL00005551
L. Molnár, Selected preserver problems on algebraic structures of linear operators and on function spaces, Lecture Notes in Mathematics, vol. 1895, Springer-Verlag, Berlin, 2007. MR 2267033
C. C. Paige and M. Wei, History and generality of the $\textrm {CS}$ decomposition, Linear Algebra Appl. 208/209 (1994), 303–326. MR 1287355, DOI 10.1016/0024-3795(94)90446-4