9 papers
Weighted homomorphisms between C*-algebras
Eusebio Gardella, Hannes Thiel
We show that a bounded, linear map between C*-algebras is a weighted -homomorphism (the central compression of a -homomorphism) if and only if it preserves zero-product…
Covering dimension of Cuntz semigroups II
Hannes Thiel, Eduard Vilalta
We show that the dimension of the Cuntz semigroup of a C*-algebra is determined by the dimensions of the Cuntz semigroups of its separable sub-C*-algebras. This allows us to remove…
Covering dimension of Cuntz semigroups
Hannes Thiel, Eduard Vilalta
We introduce a notion of covering dimension for Cuntz semigroups of C*-algebras. This dimension is always bounded by the nuclear dimension of the C*-algebra, and for subhomogeneous…
Generators in -stable C*-algebras of real rank zero
Hannes Thiel
We show that every separable C*-algebra of real rank zero that tensorially absorbs the Jiang-Su algebra contains a dense set of generators. It follows that in every classifiable, s…
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…