Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-20T15:25:17.151Z Has data issue: false hasContentIssue false
  • English
  • Français

Weakness of the Topology of a JB*-Algebra

Published online by Cambridge University Press:  20 November 2018

Ali Bensebah
Ali Bensebah*
Affiliation:
Department of Mathematics and Statistics University of Montreal, CP. 6128 Succ. A Montreal, Quebec, Canada, H3C 3J7
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.

The main purpose of this paper is to prove, that the topology of any (non-complete) algebra norm on a JB* -algebra is stronger than the topology of the usual norm. The proof of this theorem consists of an adaptation of the recent Rodriguez proof [8] that every homomorphism from a complex normed (associative) Q-algebra onto a B*-algebra is continuous.

Keywords

46H70
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 35 , Issue 4 , 01 December 1992 , pp. 449 - 454
Copyright
Copyright © Canadian Mathematical Society 1992

References

1. Bonsall, EF. and Duncan, J., Complete Normed Algebras, Springer-Verlag, 1973.Google Scholar
2. Cleveland, S. B., Homomorphisms of non-commutative *-algebras, Pacific J. Math. 13(1963), 1097–1109.Google Scholar
3. Jacobson, N., Structure and Representation of Jordan Algebras, A.M.S. Colloquium publications 39, Providence, Rhode Island, 1968.Google Scholar
4. Me Crimmon, K., The radical of a Jordan algebra, Proc. Nat. Acad. Sci. USA(1969), 671–678.Google Scholar
5. Putter, P. S. and Yood, B., Banach Jordan *-algebras, Proc. London Math. Soc. 41(1980), 21–44.Google Scholar
6. Ransford, T.J., A short proof of Johnson 's uniqueness-of-norm theorem, Bull. London Math. Soc. 21(1989), 487–488.Google Scholar
7. Rickart, C. E., General Theory of Banach Algebras, D. Van Nostrand, 1960.Google Scholar
8. Rodriguez, A. P., Automatic continuity with application to C*-algebras, Math. Proc. Camb. Phil. Soc. 107(1990), 345–347.Google Scholar
9. Wright, J. D. M., Jordan C-algebras, Michigan Math. J. 24(1977), 291–302.Google Scholar
10. Yood, B., Homomorphisms on normed algebras, Pacific J. Math. 8(1958), 373–381.Google Scholar
11. Youngson, M.A., A Vidav theorem for Banach Jordan algebras, Math. Proc. Camb. Phil. Soc. 84(1978), 263–272.Google Scholar
12. Youngson, M.A., Hermitian operators on Banach Jordan algebras, Proc. Edin. Math. Soc. 22(1979), 169– 180.Google Scholar