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The generalized state space of a commutative C*-algebra, denoted SH(C(X)), is the set of positive unital maps from C(X) to the algebra B(H) of bounded linear operators on a Hilbert space H. C*-convexity is one of several non-commutative analogs of convexity which have been discussed in this context. We show that a C*-extreme point of SH(C(X)) satisfies a certain spectral condition on the operators in the range of an associated measure, which is a positive operator-valued measure on X. We then show that C*-extreme maps from C(X) into K+, the C*-algebra generated by the compact and scalar operators, are multiplicative, generalizing a result of D. Farenick and P. Morenz.
Adviser: Professor David R. Pitts