Maximally unitarily mixed states on a C*-algebra

Robert J Archbold, Leonel Robert, Aaron Tikuisis

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Pages (from-to)187-211
Number of pages25
JournalJournal of Operator Theory
Volume80
Issue number1
DOIs
Publication statusPublished - 1 Aug 2018

Keywords

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

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