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 |
Bibliographical note
A.T. was partially supported by an NSERC Postdoctoral Fellowshipand through the EPSRC grant EP/N00874X/1.
Keywords
- States of C*-algebras
- Unitary mixings
- Dixmier property