Abstract
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.
Original language | English |
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Pages (from-to) | 39-51 |
Number of pages | 12 |
Journal | Journal of Operator Theory |
Volume | 45 |
Publication status | Published - 2001 |
Keywords
- C*-algebra
- vector functional
- pure functional
- antiliminal
- prime
- PURE STATES