Geometric structure of dimension functions of certain continuous fields

Ramon Antoine; Joan Bosa; Francesc Perera; Henning Petzka

doi:10.1016/j.jfa.2013.09.013

Geometric structure of dimension functions of certain continuous fields

Ramon Antoine, Joan Bosa, Francesc Perera, Henning Petzka

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

4 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 language	English
Pages (from-to)	2403-2423
Journal	Journal of Functional Analysis
Volume	266
Issue number	4
DOIs	https://doi.org/10.1016/j.jfa.2013.09.013
Publication status	Published - 15 Feb 2014

Keywords

C -algebras *
Continuous fields
Cuntz semigroup
Dimension functions

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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. {\textcopyright} 2013 Elsevier Inc.",

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author = "Ramon Antoine and Joan Bosa and Francesc Perera and Henning Petzka",

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doi = "10.1016/j.jfa.2013.09.013",

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TY - JOUR

T1 - Geometric structure of dimension functions of certain continuous fields

AU - Antoine, Ramon

AU - Bosa, Joan

AU - Perera, Francesc

AU - Petzka, Henning

PY - 2014/2/15

Y1 - 2014/2/15

N2 - 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.

AB - 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.

KW - C -algebras

KW - Continuous fields

KW - Cuntz semigroup

KW - Dimension functions

U2 - 10.1016/j.jfa.2013.09.013

DO - 10.1016/j.jfa.2013.09.013

M3 - Article

VL - 266

SP - 2403

EP - 2423

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

SN - 0022-1236

IS - 4

ER -