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Non-unital Banach Jordan algebras and C*-triple systems

Published online by Cambridge University Press:  20 January 2009

M. A. Youngson
M. A. Youngson
Affiliation:
Department of MathematicsHeriot-Watt UniversityEdinburgh
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The definition of a suitable Jordan analogue of C*-algebras (which we call JB*-algebras in this paper) was recently suggested by Kaplansky (see (26)). The theory of unital JB*-algebras is now comparatively well understood due to the work of Alfsen, Shultz and Størmer (1) from which a Gelfand-Neumark theorem for unital JB*-algebras can be obtained (26). Independently, from work on simply connected symmetric complex Banach manifolds with base point, Kaup introduced the definition of C*-triple systems in (14) and subsequently in (7) it was shown that every unital JB*-algebra is a C*-triple system. In this paper, we wish to extend this result to show that every JB*-algebra is a C*-triple system.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 24 , Issue 1 , February 1981 , pp. 19 - 29
Copyright
Copyright © Edinburgh Mathematical Society 1981

References

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