### 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

## Cite this

Archbold, R. J., & Shah, M. H. (2001). Limits of vector functionals.

*Journal of Operator Theory*,*45*, 39-51.