Geodesic
N Subspaces
Canadian journal of mathematics, Tome 40 (1988) no. 1, pp. 38-54

Voir la notice de l'article provenant de la source Cambridge University Press

It is a well-known fact (cf., for instance Lemma 7.3.1 of [8], and also [2] and [4] ) that if M and N are closed subspaces of a finite-dimensional Hilbert space, and if M and N are in ‘generic’ position (i.e., any two of the four subspaces M, M⊥ , N, N⊥ have trivial intersection), then N is the graph of a linear isomorphism of M onto M⊥ . To be sure, there exist infinite-dimensional versions of this, where one must allow for unbounded operators in case the ‘gap’ between M and N is zero, in the sense of Kato [7]. (There is an extensive literature on pairs of subspaces, [2], [3], [4], [6] and [7], to cite a few; for a fairly extensive bibliography, see [3].)This paper addresses itself to the case of n (2 ≦ n< ∞) subspaces. 
Sunder, V. S. N Subspaces. Canadian journal of mathematics, Tome 40 (1988) no. 1, pp. 38-54. doi: 10.4153/CJM-1988-002-0
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[1] 1. Davis, C., Generators of the ring of bounded operators, Proc. Amer. Math. Soc.. 6 (1955), 970–972. Google Scholar

[2] 2. Davis, C., Separation of two linear subspaces, Acta Sci. Math. Szeged. 19 (1958), 172–187. Google Scholar

[3] 3. Davis, C. and Kahan, W. M., Rotation of eigenvectors, SIAM J. Numer. Anal. 7 (1970), 1–16. Google Scholar

[4] 4. Halmos, P. R., Two subspaces, Trans. Amer. Math. Soc. 144 (1969), 381–389. Google Scholar

[5] 5. Hotelling, H., Relations between two sets of variables, Biometrika. 28 (1936), 321–377. Google Scholar

[6] 6. Jordan, C., Essai sur la géométrie an dimensions, Bull. Soc. Math. France. 3 (1875), 103–174. Google Scholar

[7] 7. Kato, T., Perturbation theory for linear operators (Springer, Berlin, 1966). Google Scholar

[8] 8. Murray, F.J. and von Neumann, J., On rings of operators, Ann. of Math. 37 (1936), 116–229. Google Scholar

[9] 9. Roy, S. N., Some aspects of multivariate analysis (Wiley, New York, 1958). Google Scholar

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