### Abstract

We investigate the set of maximally mixed states of a C*-algebra, extending previous work by Alberti on von Neumann algebras. We show that, unlike for von Neumann algebras, the set of maximally mixed states of a C*-algebra may fail to be weak* closed. We obtain, however, a concrete description of the weak* closure of this set, in terms of tracial states and states which factor through simple traceless quotients. For C*-algebras with the Dixmier property or with Hausdorff primitive spectrum we are able to advance our investigations further. We pose several questions.

Original language | English |
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Pages (from-to) | 187-211 |

Number of pages | 25 |

Journal | Journal of Operator Theory |

Volume | 80 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1 Aug 2018 |

### Keywords

- States of C*-algebras
- Unitary mixings
- Dixmier property

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## Cite this

Archbold, R. J., Robert, L., & Tikuisis, A. (2018). Maximally unitarily mixed states on a C*-algebra.

*Journal of Operator Theory*,*80*(1), 187-211. https://doi.org/10.7900/jot.2017sep24.2168