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Jordan Subalgebras of Banach algebras

Published online by Cambridge University Press:  20 January 2009

F. F. Bonsall
F. F. Bonsall
Affiliation:
University of Edinburgh
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We recall that a JC-algebra (Størmer (3)) is a norm closed Jordan algebra of self-adjoint operators on a Hilbert space. Recently, Alfsen, Shultz, and Størmer (1) have introduced a class of abstract normed Jordan algebras called JB-algebras, and have proved that every special JB-algebra is isometrically isomorphic to a JC-algebra. We show that this result brings to a satisfactory conclusion the discussion in (2) of certain wedges W in Banach algebras and their related Jordan algebras W–W, and leads to two characterisations of the bicontinuously isomorphic images of JC-algebras.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 21 , Issue 2 , September 1978 , pp. 103 - 110
Copyright
Copyright © Edinburgh Mathematical Society 1978

References

REFERENCES

(1) Alfsen, E. M., Shultz, F. W., and Størmer, E., A Gelfand-Neumark theorem for Jordan algebras, Advances in Math. 28 (1978), 11–56.CrossRefGoogle Scholar
(2) Bonsall, F. F., Locally multiplicative wedges in Banach algebras, Proc. London Math. Soc. (3) 30 (1975), 239–256.CrossRefGoogle Scholar
(3) StøRmer, E., On the Jordan structure of C*-algebras, Trans. Amer. Math. Soc. 120 (1965), 438–447.Google Scholar