The space of tracial states on a C∗-algebra

Bruce Blackadar; Mikael Rørdam

doi:10.1016/j.exmath.2024.125618

The space of tracial states on a C^∗-algebra

Bruce Blackadar, Mikael Rørdam^*

^*Corresponding author af dette arbejde

Institut for Matematiske Fag

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › peer review

1 Citationer (Scopus)

Abstract

We give a simple and elementary proof that the tracial state space of a unital C^∗-algebra is a Choquet simplex, using the center-valued trace on a finite von Neumann algebra.

Originalsprog	Engelsk
Artikelnummer	125618
Tidsskrift	Expositiones Mathematicae
ISSN	0723-0869
DOI	https://doi.org/10.1016/j.exmath.2024.125618
Status	E-pub ahead of print - 2024

Bibliografisk note

Funding Information:
The second named author was supported by a research grant from the Danish Council for Independent Research, Natural Sciences.

Publisher Copyright:
© 2024 Elsevier GmbH

Adgang til dokumentet

10.1016/j.exmath.2024.125618

Citationsformater

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title = "The space of tracial states on a C∗-algebra",

abstract = "We give a simple and elementary proof that the tracial state space of a unital C∗-algebra is a Choquet simplex, using the center-valued trace on a finite von Neumann algebra.",

keywords = "C*-algebra, Choquet simplex, Traces",

author = "Bruce Blackadar and Mikael R{\o}rdam",

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journal = "Expositiones Mathematicae",

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AU - Rørdam, Mikael

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AB - We give a simple and elementary proof that the tracial state space of a unital C∗-algebra is a Choquet simplex, using the center-valued trace on a finite von Neumann algebra.

KW - C-algebra

KW - Choquet simplex

KW - Traces

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DO - 10.1016/j.exmath.2024.125618

M3 - Journal article

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JO - Expositiones Mathematicae

JF - Expositiones Mathematicae

SN - 0723-0869

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