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.
Bibliographical noteA.T. was partially supported by an NSERC Postdoctoral Fellowship
and through the EPSRC grant EP/N00874X/1.
- States of C*-algebras
- Unitary mixings
- Dixmier property