Cuntz semigroups of ultraproduct C∗-algebras

Ramon Antoine*, Francesc Perera, Hannes Thiel

*Corresponding author for this work

Research output: Contribution to journalArticleResearchpeer-review

5 Citations (Scopus)


We prove that the category of abstract Cuntz semigroups is bicomplete. As a consequence, the category admits products and ultraproducts. We further show that the scaled Cuntz semigroup of the (ultra)product of a family of (Formula presented.) -algebras agrees with the (ultra)product of the scaled Cuntz semigroups of the involved (Formula presented.) -algebras. As applications of our results, we compute the non-stable K-Theory of general (ultra)products of (Formula presented.) -algebras and we characterize when ultraproducts are simple. We also give criteria that determine order properties of these objects, such as almost unperforation.

Original languageEnglish
Pages (from-to)994-1029
Number of pages36
JournalJournal of the London Mathematical Society
Issue number3
Publication statusPublished - Dec 2020


  • 03C20
  • 06B30
  • 06B35
  • 06F05
  • 18A30
  • 18A35
  • 18B35
  • 19K14
  • 46L05
  • 46M07 (primary)
  • 46M15
  • 46M40 (secondary)


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