Quasidiagonal traces on exact C-algebras

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Abstract

Recently, it was proved by Tikuisis, White and Winter that any faithful trace on a separable, nuclear C-algebra in the UCT class is quasidiagonal. Building on their work, we generalise the result, and show that any faithful, amenable trace on a separable, exact C-algebra in the UCT class is quasidiagonal. We also prove that any amenable trace on a separable, exact, quasidiagonal C-algebra in the UCT class is quasidiagonal.

Original languageEnglish
JournalJournal of Functional Analysis
Volume272
Issue number3
Pages (from-to)1104-1120
ISSN0022-1236
DOIs
Publication statusPublished - 2017

Keywords

  • Nuclear maps
  • Order zero maps
  • Quasidiagonal C-algebras
  • Traces

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