The cuntz semigroup and stability of close C*-algebras

Francesc Perera, Andrew Toms, Stuart White, Wilhelm Winter

Research output: Contribution to journalArticleResearchpeer-review

4 Citations (Scopus)

Abstract

We prove that separable C*-algebras whiC*-algebras provided that one algebra has stable rank one; close C*-algebras must have affinely homeomorphic spaces of lower-semicontinuous quasitraces; strict comparison is preserved by sufficient closeness of C*-algebras. We also examine C*-algebras which have a positive answer to Kadison's Similarity Problem, as these algebras are completely close whenever they are close. A sample consequence is that sufficiently close C*-algebras have isomorphic Cuntz semigroups when one algebra absorbs the Jiang-Su algebra tensorially. © 2014 Mathematical Sciences Publishers.
Original languageEnglish
Pages (from-to)929-952
JournalAnalysis and PDE
Volume7
Issue number4
DOIs
Publication statusPublished - 1 Jan 2014

Keywords

  • C*-algebras
  • Cuntz semigroup
  • Perturbation
  • Quasitraces
  • Stability
  • Traces

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