Limits of vector functionals

For vector functionals on a C*-algebra of operators, we prove an analogue o f Glimm's vector state space theorem. We deduce that a C*-algebra is prime and antiliminal if and only if the pure functionals are w*-dense in the uni t ball of the dual. We also give a necessary and sufficient condition for a convex combination of inequivalent pure functionals to be a w*-limit of pu re functionals.