Hostname: page-component-6bf8c574d5-r8w4l Total loading time: 0 Render date: 2025-03-05T05:32:50.599Z Has data issue: false hasContentIssue false
  • English
  • Français

On compact action in JB-algebras

Published online by Cambridge University Press:  20 January 2009

L. J. Bunce
L. J. Bunce
Affiliation:
Mathematics DepartmentUniversity of Reading
Rights & Permissions [Opens in a new window]

Extract

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.

A real Jordan algebra which is also a Banach space with a norm which satisfies

for each pair a, b of elements, is said to be a JB-algebra. A JB-algebra which is also a Banach dual space is said to be a JBW-algebra.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 26 , Issue 3 , October 1983 , pp. 353 - 360
Copyright
Copyright © Edinburgh Mathematical Society 1983

References

REFERENCES

1.Alexander, J. A., Compact Banach algebras, Proc. London Math. Soc. (3) 18 (1968), 1–18.CrossRefGoogle Scholar
2.Alfsen, E. M., Shultz, F. W. and Stormer, E., A Gelfand Neumark theorem for Jordan algebras, Advances in Math. 28 (1978), 11–56.CrossRefGoogle Scholar
3.Behncke, H., Hermitian Jordan Banach algebras, J. London Math. Soc. (2) 20 (1979), 306–312.Google Scholar
4.Bunce, L. J., Theory and structure of dual JB-algebras, Math. Zeit. (to appear).Google Scholar
5.Dixmier, J., C*-Algebras (North-Holland, Amsterdam, 1977).Google Scholar
6.Dunford, N. and Schwarz, J. T., Linear Operators, Part I (Interscience, 1958).Google Scholar
7.Edwards, C. M., Ideal theory in JB-algebras, J. London Math. Soc. (2) 16 (1977), 507–513.CrossRefGoogle Scholar
8.Edwards, C. M., On the facial structure of a JB-algebra, J. London Math. Soc. (2) 19 (1979), 335–344.CrossRefGoogle Scholar
9.Edwards, C. M., On the centres of hereditary JBW-subalgebras of a JBW-algebra, Math. Proc. Cambs. Philos. Soc. 85 (1979), 317–325.CrossRefGoogle Scholar
10.Effros, E. and Stormer, E., Jordan algebras of self adjoint operators, Trans. Amer. Math. Soc. 127 (1967), 312–315.CrossRefGoogle Scholar
11.Hanche-Olsen, H., A note on the bidual of a JB-algebra, Math. Zeit. 175 (1980), 29–31.CrossRefGoogle Scholar
12.Jacobson, N., Structure and Representations of Jordan Algebras (Amer. Math. Soc. Colloq. Publications 39, Providence R.I. 1968).CrossRefGoogle Scholar
13.Kaplansky, I., Dual rings, Duke Math. J. 6 (1949), 399–418.Google Scholar
14.Smith, R. R., On non-unital Jordan Banach algebras, Math. Proc. Cambs. Philos. Soc. 82 (1977), 375–380.CrossRefGoogle Scholar
15.Shultz, F. W., On normed Jordan algebras which are Banach dual spaces, J. Functional Analysis 31 (1979), 360–376.CrossRefGoogle Scholar
16.Topping, D., Jordan Algebras of Self Adjoint Operators (Mem. Amer. Math. Soc. 53, 1965).CrossRefGoogle Scholar
17.Topping, D., An isomorphism invariant for spin factors, J. Math. Mech. 15 (1965), 1055–1063.Google Scholar
18.Wright, J. D. M., Jordan C*-algebras, Michigan Math. J. 24 (1977), 291–302.CrossRefGoogle Scholar
19.Youngson, M. A., Hermitian operators on Banach Jordan algebras, Proc. Edinburgh Math. Soc. 27 (1979), 169–180.CrossRefGoogle Scholar