47 citations · 84 across the 10 of their papers we have counts for
14 papers · 1 filter
Pure C*-algebras
Ramon Antoine, Francesc Perera, Hannes Thiel +1
We demonstrate that pure C*-algebras form a robust class by proving that pureness follows from very weak comparison and divisibility properties. Using this, we show that every simp…
Traces on ultrapowers of C*-algebras
Ramon Antoine, Francesc Perera, Leonel Robert +1
Using Cuntz semigroup techniques, we characterize when limit traces are dense in the space of all traces on a free ultrapower of a C*-algebra. More generally, we consider density o…
Edwards' condition for quasitraces on C*-algebras
Ramon Antoine, Francesc Perera, Leonel Robert +1
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 proble…
Cuntz semigroups of ultraproduct C*-algebras
Ramon Antoine, Francesc Perera, Hannes Thiel
We prove that the category of abstract Cuntz semigroups is bicomplete. As a consequence, the category admits products and ultraproducts. We further show that the scaled Cuntz semig…
Abstract Bivariant Cuntz Semigroups II
Ramon Antoine, Francesc Perera, Hannes Thiel
We previously showed that abstract Cuntz semigroups form a closed symmetric monoidal category. This automatically provides additional structure in the category, such as a compositi…
C*-algebras of stable rank one and their Cuntz semigroups
Ramon Antoine, Francesc Perera, Leonel Robert +1
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…