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 language | English |
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Pages (from-to) | 2403-2423 |
Journal | Journal of Functional Analysis |
Volume | 266 |
Issue number | 4 |
DOIs | |
Publication status | Published - 15 Feb 2014 |
Keywords
- C -algebras *
- Continuous fields
- Cuntz semigroup
- Dimension functions