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

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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]). 
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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     title = {Another {Weak} {Stone-Weierstrass} {Theorem} for {C} {*-Algebras}},
     journal = {Canadian mathematical bulletin},
     pages = {355--357},
     year = {1972},
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     doi = {10.4153/CMB-1972-064-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1972-064-x/}
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