Geometric structure of dimension functions of certain continuous fields

Ramon Antoine, Joan Bosa, Francesc Perera, Henning Petzka

Research output: Contribution to journalArticleResearchpeer-review

5 Citations (Scopus)

Abstract

For a continuous field of C*-algebras A, we give a criterion to ensure that the stable rank of A is one. In the particular case of a trivial field this leads to a characterization of stable rank one, completing accomplishments by Nagisa, Osaka and Phillips. Further, for certain continuous fields of C*-algebras, we study when the Cuntz semigroup satisfies the Riesz interpolation property, and we also analyze the structure of its functionals. As an application, we obtain a positive answer to a conjecture posed by Blackadar and Handelman in a variety of situations. © 2013 Elsevier Inc.
Original languageEnglish
Pages (from-to)2403-2423
JournalJournal of Functional Analysis
Volume266
Issue number4
DOIs
Publication statusPublished - 15 Feb 2014

Keywords

  • C -algebras *
  • Continuous fields
  • Cuntz semigroup
  • Dimension functions

Fingerprint

Dive into the research topics of 'Geometric structure of dimension functions of certain continuous fields'. Together they form a unique fingerprint.

Cite this