Hostname: page-component-848d4c4894-x24gv Total loading time: 0 Render date: 2024-06-01T21:45:25.119Z Has data issue: false hasContentIssue false
  • English
  • Français

Linear Transformations on Symmetric Spaces II

Published online by Cambridge University Press:  20 November 2018

Ming–Huat Lim
Ming–Huat Lim*
Affiliation:
Department of Mathematics, University of Malaya, Kuala Lumpur, Malaysia
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Keywords

15A69
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 45 , Issue 2 , 01 April 1993 , pp. 357 - 368
Copyright
Copyright © Canadian Mathematical Society 1993

References

1. Chan, G.H. and Lim, M.H., Linear transformations on tensor spaces, Linear and Multilinear Alg. 14(1983), 3–9.Google Scholar
2. Cummings, L.J., Decomposable symmetric tensors, Pacific J. Math. 35(1970), 65–11.Google Scholar
3. Cummings, L.J., Transformations of symmetric tensors, Pacific J. Math. 42(1972), 603–613.Google Scholar
4. Hopf, H., Système symmetrischer Bilinearformen und euklidische Modelle der projectiven Raume, Vierteljschr Naturforsch. Ges, Zurich 85(1940), 165–177.Google Scholar
5. James, I.M., Euclidean models of projective Spaces, Bull London Math. Soc. 3(1971), 257–276.Google Scholar
6. Lim, M.H., Linear transformations on symmetric spaces, Pacific J. Math. 55(1974), 499–505.Google Scholar
7. Lim, M.H., A note on maximal decomposable subspaces of symmetric spaces, Bull. London Math. Soc. 7(1975), 289–293.Google Scholar
8. Lim, M.H., Linear transformations on symmetry classes of tensors, Linear and Multilinear Alg. 3(1976), 267–280.Google Scholar
9. Mahowald, M., On the embeddability of the real projective spaces, Proc. Amer. Math. Soc. 13(1962), 763–764.Google Scholar
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. Marcus, M., Finite Dimensional Multilinear Algebra, Part 1, Marcel Dekker, New York, 1973.Google Scholar
12. Massey, W.S., On the embeddability of the real projective spaces in Euclidean space, Pacific J. Math. 9(1959), 783–789.Google Scholar