Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-29T19:05:50.492Z Has data issue: false hasContentIssue false
  • English
  • Français

The connection between the universal enveloping C*-algebra and the universal enveloping von Neumann algebra of a JW-algebra

Published online by Cambridge University Press:  24 October 2008

Fatmah B. Jamjoom
Fatmah B. Jamjoom
Affiliation:
Department of Mathematics, King Saud University, Riyadh, Saudi Arabia
Get access Rights & Permissions [Opens in a new window]

Abstract

This article aims to study the relationship between the universal enveloping C*-algebra C*(M) and the universal enveloping von Neumann algebra W*(M), when M is a JW-algebra. In our main result (Theorem 2·7) we show that C*(M) can be realized as the C*-subalgebra of W*(M) generated by M.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 112 , Issue 3 , November 1992 , pp. 575 - 579
Copyright
Copyright © Cambridge Philosophical Society 1992

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Bunce, L. J. and Wright, J. D. M.. Quantum measures and states on Jordan algebras. Commun. Math. Phys. 98 (1985), 187–202.CrossRefGoogle Scholar
[2]Bunce, L. J. and Wright, J. D. W.. Introduction to the K-theory of Jordan C*-algebras. Quart. J. Math. Oxford Ser. (2) 40 (1989), 377–398.CrossRefGoogle Scholar
[3]Hanche-Olsen, H. and Størmer, E.. Jordan Operator Algebras (Pitman, 1984).Google Scholar
[4]Kadison, R. V. and Ringrose, J. R.. Fundamentals of the Theory of Operator Algebras, vol. 2 (Academic Press, 1986).Google Scholar
[5]Stacey, P. J.. Type I2 JBW-algebras. Quart. J. Math. Oxford Ser. (2) 33 (1982), 115–127.CrossRefGoogle Scholar
[6]Stømer, E.. Jordan algebra of Type I. Ada. Math. 115 (1966), 165–184.Google Scholar
[7]Stømer, E.. Irreducible Jordan algebras of self adjoint operators. Trans. Amer. Math. Soc. 130 (1968), 153–166.CrossRefGoogle Scholar