Geodesic
Another Weak Stone-Weierstrass Theorem for C *-Algebras
Canadian mathematical bulletin, Tome 15 (1972) no. 3, pp. 355-357

Voir la notice de l'article provenant de la source Cambridge University Press

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]). 
Elliott, George A. Another Weak Stone-Weierstrass Theorem for C *-Algebras. Canadian mathematical bulletin, Tome 15 (1972) no. 3, pp. 355-357. doi: 10.4153/CMB-1972-064-x
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