C*-algebras of stable rank one and their Cuntz semigroups

Fuente: arXiv
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Hauptverfasser: Antoine, Ramon, Perera, Francesc, Robert, Leonel, Thiel, Hannes
Format: Preprint
Veröffentlicht: 2018
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author Antoine, Ramon
Perera, Francesc
Robert, Leonel
Thiel, Hannes
author_facet Antoine, Ramon
Perera, Francesc
Robert, Leonel
Thiel, Hannes
contents The uncovering of new structure on the Cuntz semigroup of a C*-algebra of stable rank one leads to several applications: We answer affirmatively, for the class of stable rank one C*-algebras, a conjecture by Blackadar and Handelman on dimension functions, the Global Glimm Halving problem, and the problem of realizing functions on the cone of 2-quasitraces as ranks of Cuntz semigroup elements. We also gain new insights into the comparability properties of positive elements in C*-algebras of stable rank one.
format Preprint
id arxiv_https___arxiv_org_abs_1809_03984
institution arXiv
publishDate 2018
record_format arxiv
spellingShingle C*-algebras of stable rank one and their Cuntz semigroups
Antoine, Ramon
Perera, Francesc
Robert, Leonel
Thiel, Hannes
Operator Algebras
46L05 (Primary), 06B35, 06F05, 19K14, 46L08, 46L35 (Secondary)
The uncovering of new structure on the Cuntz semigroup of a C*-algebra of stable rank one leads to several applications: We answer affirmatively, for the class of stable rank one C*-algebras, a conjecture by Blackadar and Handelman on dimension functions, the Global Glimm Halving problem, and the problem of realizing functions on the cone of 2-quasitraces as ranks of Cuntz semigroup elements. We also gain new insights into the comparability properties of positive elements in C*-algebras of stable rank one.
title C*-algebras of stable rank one and their Cuntz semigroups
topic Operator Algebras
46L05 (Primary), 06B35, 06F05, 19K14, 46L08, 46L35 (Secondary)
url https://arxiv.org/abs/1809.03984