Edwards' condition for quasitraces on C∗-algebras

Ramon Antoine; Francesc Perera; Leonel Robert; Hannes Thiel

doi:10.1017/prm.2020.26

Edwards' condition for quasitraces on C∗-algebras

Ramon Antoine, Francesc Perera, Leonel Robert, Hannes Thiel

Department of Mathematics

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

10 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	525-547
Number of pages	23
Journal	Proceedings of the Royal Society of Edinburgh Section A: Mathematics
Volume	151
Issue number	2
DOIs	https://doi.org/10.1017/prm.2020.26
Publication status	Published - Apr 2021

Keywords

Cuntz semigroups
C∗-algebras
Quasitraces
Traces

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10.1017/prm.2020.26Licence: CC BY

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abstract = "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 = "Cuntz semigroups, C∗-algebras, Quasitraces, Traces",

author = "Ramon Antoine and Francesc Perera and Leonel Robert and Hannes Thiel",

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AU - Antoine, Ramon

AU - Perera, Francesc

AU - Robert, Leonel

AU - Thiel, Hannes

PY - 2021/4

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N2 - 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.

AB - 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.

KW - Cuntz semigroups

KW - C∗-algebras

KW - Quasitraces

KW - Traces

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DO - 10.1017/prm.2020.26

M3 - Article

AN - SCOPUS:85083325434

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EP - 547

JO - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

JF - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

IS - 2

ER -

Edwards' condition for quasitraces on C∗-algebras

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Keywords

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