### Abstract

Original language | English |
---|---|

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 |

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### Keywords

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

### Cite this

*Journal of Operator Theory*,

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

**Maximally unitarily mixed states on a C*-algebra.** / Archbold, Robert J; Robert, Leonel; Tikuisis, Aaron.

Research output: Contribution to journal › Article

*Journal of Operator Theory*, vol. 80, no. 1, pp. 187-211. https://doi.org/10.7900/jot.2017sep24.2168

}

TY - JOUR

T1 - Maximally unitarily mixed states on a C*-algebra

AU - Archbold, Robert J

AU - Robert, Leonel

AU - Tikuisis, Aaron

N1 - A.T. was partially supported by an NSERC Postdoctoral Fellowship and through the EPSRC grant EP/N00874X/1.

PY - 2018/8/1

Y1 - 2018/8/1

N2 - 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.

AB - 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.

KW - States of C-algebras

KW - Unitary mixings

KW - Dixmier property

U2 - 10.7900/jot.2017sep24.2168

DO - 10.7900/jot.2017sep24.2168

M3 - Article

VL - 80

SP - 187

EP - 211

JO - Journal of Operator Theory

JF - Journal of Operator Theory

SN - 0379-4024

IS - 1

ER -