Abstract
We generalize the setting of the Stone-Weierstrass problem to the cone CP(A, H) of all completely positive linear maps of a C*-algebra A into the C*-algebra B(H) of all bounded linear operators on a Hilbert space H, and give some equivalent conditions for the problem. As a consequence, a new generalized spectrum, containing pure states and irreducible representations, will be introduced.
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Fujimoto, I., Takahasi, S.E. Equivalent conditions for the general Stone-Weierstrass problem. Manuscripta Math 53, 217–224 (1985). https://doi.org/10.1007/BF01626397
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DOI: https://doi.org/10.1007/BF01626397