Geodesic
Linear Transformations on Symmetric Spaces II
Canadian journal of mathematics, Tome 45 (1993) no. 2, pp. 357-368

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

Let U be a finite dimensional vector space over an infinite field F. Let U (r) denote the r–th symmetric product space over U. Let T: U(r) → U(s) be a linear transformation which sends nonzero decomposable elements to nonzero decomposable elements. Let dim U ≥ s + 1. Then we obtain the structure of T for the following cases: (I) F is algebraically closed, (II) F is the real field, and (III) T is injective.
DOI : 10.4153/CJM-1993-017-2
Mots-clés : 15A69 
Lim, Ming–Huat. Linear Transformations on Symmetric Spaces II. Canadian journal of mathematics, Tome 45 (1993) no. 2, pp. 357-368. doi: 10.4153/CJM-1993-017-2
@article{10_4153_CJM_1993_017_2,
     author = {Lim, Ming{\textendash}Huat},
     title = {Linear {Transformations} on {Symmetric} {Spaces} {II}},
     journal = {Canadian journal of mathematics},
     pages = {357--368},
     year = {1993},
     volume = {45},
     number = {2},
     doi = {10.4153/CJM-1993-017-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1993-017-2/}
}
TY  - JOUR
AU  - Lim, Ming–Huat
TI  - Linear Transformations on Symmetric Spaces II
JO  - Canadian journal of mathematics
PY  - 1993
SP  - 357
EP  - 368
VL  - 45
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1993-017-2/
DO  - 10.4153/CJM-1993-017-2
ID  - 10_4153_CJM_1993_017_2
ER  - 
%0 Journal Article
%A Lim, Ming–Huat
%T Linear Transformations on Symmetric Spaces II
%J Canadian journal of mathematics
%D 1993
%P 357-368
%V 45
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1993-017-2/
%R 10.4153/CJM-1993-017-2
%F 10_4153_CJM_1993_017_2

[1] 1. Chan, G.H. and Lim, M.H., Linear transformations on tensor spaces, Linear and Multilinear Alg. 14(1983), 3–9. Google Scholar

[2] 2. Cummings, L.J., Decomposable symmetric tensors, Pacific J. Math. 35(1970), 65–11. Google Scholar

[3] 3. Cummings, L.J., Transformations of symmetric tensors, Pacific J. Math. 42(1972), 603–613. Google Scholar

[4] 4. Hopf, H., Système symmetrischer Bilinearformen und euklidische Modelle der projectiven Raume, Vierteljschr Naturforsch. Ges, Zurich 85(1940), 165–177. Google Scholar

[5] 5. James, I.M., Euclidean models of projective Spaces, Bull London Math. Soc. 3(1971), 257–276. Google Scholar

[6] 6. Lim, M.H., Linear transformations on symmetric spaces, Pacific J. Math. 55(1974), 499–505. Google Scholar

[7] 7. Lim, M.H., A note on maximal decomposable subspaces of symmetric spaces, Bull. London Math. Soc. 7(1975), 289–293. Google Scholar

[8] 8. Lim, M.H., Linear transformations on symmetry classes of tensors, Linear and Multilinear Alg. 3(1976), 267–280. Google Scholar

[9] 9. Mahowald, M., On the embeddability of the real projective spaces, Proc. Amer. Math. Soc. 13(1962), 763–764. Google Scholar

[10] 10. Marcus, M., Linear transformations on matrices, Journal of Research of the National Bureau of Standards (U.S.) (B) 75(1971), 107–113. Google Scholar

[11] 11. Marcus, M., Finite Dimensional Multilinear Algebra, Part 1, Marcel Dekker, New York, 1973. Google Scholar

[12] 12. Massey, W.S., On the embeddability of the real projective spaces in Euclidean space, Pacific J. Math. 9(1959), 783–789. Google Scholar

Cité par Sources :