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

Departament de Matemàtiques

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Resum

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.

Idioma original	Anglès
Pàgines (de-a)	525-547
Nombre de pàgines	23
Revista	Proceedings of the Royal Society of Edinburgh Section A: Mathematics
Volum	151
Número	2
DOIs	https://doi.org/10.1017/prm.2020.26
Estat de la publicació	Publicada - d’abr. 2021

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10.1017/prm.2020.26Llicència: Creative Commons Reconeixement

https://ddd.uab.cat/record/306022

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title = "Edwards' condition for quasitraces on C∗-algebras",

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",

note = "Publisher Copyright: Copyright {\textcopyright} The Author(s), 2020. Published by Cambridge University Press.",

year = "2021",

month = apr,

doi = "10.1017/prm.2020.26",

language = "English",

volume = "151",

pages = "525--547",

journal = "Proceedings of the Royal Society of Edinburgh Section A: Mathematics",

issn = "0308-2105",

publisher = "Cambridge University Press",

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TY - JOUR

T1 - Edwards' condition for quasitraces on C∗-algebras

AU - Antoine, Ramon

AU - Perera, Francesc

AU - Robert, Leonel

AU - Thiel, Hannes

PY - 2021/4

Y1 - 2021/4

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

UR - http://www.scopus.com/inward/record.url?scp=85083325434&partnerID=8YFLogxK

U2 - 10.1017/prm.2020.26

DO - 10.1017/prm.2020.26

M3 - Article

AN - SCOPUS:85083325434

SN - 0308-2105

VL - 151

SP - 525

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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