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Another Weak Stone-Weierstrass Theorem for C *-Algebras

Published online by Cambridge University Press:  20 November 2018

George A. Elliott
George A. Elliott*
Affiliation:
Queen's University, Kingston, Ontario
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The purpose of this article is to present a new generalization of the classical Stone-Weierstrass theorem for commutative C*-algebras.

Under the assumption that B is a sub-C*-algebra of A separating the pure states of A and zero, Kaplansky has conjectured that B=A [4, p. 246]. He gave a proof for the case that A is postliminary ([4, Theorem 7.2]; see also [2, 11.1.8]). Glimm, Akemann, and Sakai have established the conjecture in the presence of various other additional hypotheses, most of which hold in the commutative case ([3], [1], [7]).

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 15 , Issue 3 , September 1972, pp. 355 - 357
Copyright
Copyright © Canadian Mathematical Society 1972

References

1. Akemann, C., The general Stone-Weierstrass problem, J. Functional Analysis 4 (1969), 277-294.Google Scholar
2. Dixmier, J., Les C*-algèbres et leurs représentations, Gauthier-Villars, Paris, 1964.Google Scholar
3. Glimm, J., A Stone-Weierstrass theorem for C*-algebras, Ann. of Math. 72 (1960), 216-244.Google Scholar
4. Kaplansky, I., The structure of certain operator algebras, Trans. Amer. Math. Soc. 70 (1951), 219-255.Google Scholar
5. Sakai, S., Derivations of W*-algebras, Ann. of Math. 83 (1966), 273-279.Google Scholar
6. Sakai, S., Derivations of simple C*-algebras, J. Functional Analysis 2 (1968), 202-206.Google Scholar
7. Sakai, S., On the Stone-Weierstrass theorem of C*-algebras, Tôhoku Math. J. 22 (1970), 191-199.Google Scholar
8. Sakai, S., A characterization of type I C*-algebras, Bull. Amer. Math. Soc. 72 (1965), 508-512.Google Scholar
9. Takesaki, M., On the cross-norm of the direct product of C*-algebras, Tôhoku Math. J. 16 (1964), 111-122.Google Scholar