For vector functionals on a C*-algebra of operators, we prove an analogue of 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 unit 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 pure functionals.
|Number of pages||12|
|Journal||Journal of Operator Theory|
|Publication status||Published - 2001|
- vector functional
- pure functional
- PURE STATES