47 citations · 142 across the 26 of their papers we have counts for
32 papers
The Cuntz semigroup of a ring
Ramon Antoine, Pere Ara, Joan Bosa +2
For any ring , we introduce an invariant in the form of a partially ordered abelian semigroup built from an equivalence relation on the class of countably genera…
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…
The modern theory of Cuntz semigroups of C*-algebras
Eusebio Gardella, Francesc Perera
We give a detailed introduction to the theory of Cuntz semigroups for C*-algebras. Beginning with the most basic definitions and technical lemmas, we present several results of his…
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…