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Edwards' condition for quasitraces on C*-algebras

Part of: Lattices $K$-theory and operator algebras Selfadjoint operator algebras Ordered structures

Published online by Cambridge University Press:  08 April 2020

Ramon Antoine ,
Francesc Perera ,
Leonel Robert  and
Hannes Thiel
Ramon Antoine
Affiliation:
Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193Bellaterra, Barcelona, Spain (ramon@mat.uab.cat; perera@mat.uab.cat)
Francesc Perera
Affiliation:
Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193Bellaterra, Barcelona, Spain (ramon@mat.uab.cat; perera@mat.uab.cat)
Leonel Robert
Affiliation:
Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA70504-1010, USA (lrobert@louisiana.edu)
Hannes Thiel
Affiliation:
Mathematisches Institut, Universität Münster, Einsteinstr. 62, 48149 Münster, Germany (hannes.thiel@uni-muenster.de)
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Abstract

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We prove that Cuntz semigroups of C*-algebras satisfy Edwards' condition with respect to every quasitrace. This condition is a key ingredient in the study of the realization problem of functions on the cone of quasitraces as ranks of positive elements. In the course of our investigation, we identify additional structure of the Cuntz semigroup of an arbitrary C*-algebra and of the cone of quasitraces.

Keywords

C*-algebrasTracesQuasitracesCuntz semigroups

MSC classification

Primary: 46L05: General theory of $C^*$-algebras
Secondary: 06B35: Continuous lattices and posets, applications 06F05: Ordered semigroups and monoids 19K14: $K_0$ as an ordered group, traces 46L35: Classifications of $C^*$-algebras
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 151 , Issue 2 , April 2021 , pp. 525 - 547
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
Copyright © The Author(s), 2020. Published by Cambridge University Press

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