Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-27T07:37:57.996Z Has data issue: false hasContentIssue false
  • English
  • Français

JV-Algèbres et JH*-Algèbres

Published online by Cambridge University Press:  20 November 2018

Ali Bensebah
Ali Bensebah*
Affiliation:
Département de Mathématiques et de Statistiques, Université de Montréal, C.P. 6128 succursale A, Montréal, Québec H3C 3J7
Rights & Permissions [Opens in a new window]

Résumé

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.

In the present article we generalize Theorem 2.3 of [6] in the case of JV algebras without a unit element and we obtain as a consequence that the multiplicativity of the involution ((xy)* = y*x*) in the definition of a JH*-algebra is redundant (see [3]). We end this paper with a theorem on unital JH*-algebra which is a nonassociative extension of the main result in [4].

Keywords

46H70
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 34 , Issue 4 , 01 December 1991 , pp. 447 - 455
Copyright
Copyright © Canadian Mathematical Society 1991

References

Références

1. Ambrose, W., Structure theorems for a special class ofBanach algebras, Trans. Amer. Math. Soc. 57 (1945), 364–386.Google Scholar
2. Bonsall, F. F. and Duncan, J., Numerical ranges of operators on normed spaces and of elements ofnormed algebras. Lecture Notes series 2, London Math. Soc, Cambridge, 1971.Google Scholar
3. Devapakkiam, C. V., Hilbert space methods in the theory of Jordan algebras, Math. Proc. Camb. Phil. Soc. 78 (1975), 293–300.Google Scholar
4. Ingelstam, L., Hilbert algebras with identity, Bull. Amer. Math. Soc. 69 (1963), 794–796.Google Scholar
5. Jacobson, N., Structure and representations of Jordan algebras, Amer. Math. Soc. Coll. 39.Google Scholar
6. Martinez, J. M., JV-algebras, Math. Proc. Camb. Phil. Soc. 87 (1980), 47–50.Google Scholar
7. Rodriguez, P. A., Non-associative normed algebras spanned by Hermitian elements, Proc. London Math. Soc. (3)47 (1983), 258–274.Google Scholar
8. Smiley, M. F., Real Hilbert algebras with identity, Proc. Amer. Math. Soc. 16 (1965), 440–441.Google Scholar
9. Urbanik, K. and Wright, F. B., Absolute-valued algebras, Proc. Amer. Math. Soc. 11 (1960), 861–866.Google Scholar