Abstract
Let A be a C*-algebra with identity e and let B be a C*-subalgebra of A that contains e. We show that if B separates the pure states of A, then, for each n, B also separates the set ECP(A,ℂn;I) of extremal completely positive unital maps of A into ℂn, thus giving another equivalent condition for the general Stone-Weierstrass conjecture for C*-algebras.
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Bunce, J.W. The general Stone-Weierstrass problem and extremal completely positive maps. Manuscripta Math 56, 343–351 (1986). https://doi.org/10.1007/BF01180773
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DOI: https://doi.org/10.1007/BF01180773