5 citations · 7 across the 19 of their papers we have counts for
23 papers
Super adaptable graphs and the realization problem
Pere Ara, Joan Bosa, Laurent Cantier +2
We introduce and study the family of super adaptable monoids, which includes, among many others, all conical refinement monoids that are either finitely generated, or countable, pr…
Continuous functions over a pure C*-algebra
Apurva Seth, Eduard Vilalta
Let be a compact metric space, and let be a pure -algebra. We show that is pure whenever is simple; or every quotient of is stably finite (e.…
Centrally pure C*-algebras
Francesc Perera, Hannes Thiel, Eduard Vilalta
We show that a separable C*-algebra is -stable if and only if its uncorrected central sequence algebra is pure, if and only if Kirchberg'…
An introduction to the Global Glimm Problem
Eduard Vilalta
The Global Glimm Problem lies at the heart of several open questions regarding regularity properties of C*-algebras. The problem has been open for over two decades, and has recentl…
The Global Glimm Property for C*-algebras of topological dimension zero
Ping Wong Ng, Hannes Thiel, Eduard Vilalta
We show that a C*-algebra with topological dimension zero has the Global Glimm Property (every hereditary subalgebra contains an almost full nilpotent element) if and only if it is…
Extensions of pure C*-algebras
Francesc Perera, Hannes Thiel, Eduard Vilalta
Given a closed ideal in a C*-algebra , we show that is pure if and only if and are pure. More generally, we study permanence of comparison and divisibility pro…
Strict comparison for twisted group C*-algebras
Sven Raum, Hannes Thiel, Eduard Vilalta
We prove that any reduced twisted group C*-algebra of a selfless group with the rapid decay property is selfless. As an application, we show that twisted group C*-algebras of acyli…
Z-stability of twisted group C*-algebras of nilpotent groups
Ulrik Enstad, Eduard Vilalta
We prove that the twisted group C*-algebra of a finitely generated nilpotent group is -stable if and only if it is nowhere scattered, a condition that we characterize…
Ideals, quotients, and continuity of the Cuntz semigroup for rings
Ramon Antoine, Pere Ara, Joan Bosa +2
In this paper we explore which part of the ideal lattice of a general ring is parametrized by its Cuntz semigroup and its ambient semigroup . We identify thes…
Criteria for the existence of Schwartz Gabor frames over rational lattices
Ulrik Enstad, Hannes Thiel, Eduard Vilalta
We give an explicit criterion for a rational lattice in the time-frequency plane to admit a Gabor frame with window in the Schwartz class. The criterion is an inequality formulated…
Pure *-homomorphisms
Joan Bosa, Eduard Vilalta
We introduce and study a notion of pureness for *-homomorphisms and, more generally, for cpc. order-zero maps. After providing several examples of pureness, such as "-…
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…
Ranks of soft operators in nowhere scattered C*-algebras
M. Ali Asadi-Vasfi, Hannes Thiel, Eduard Vilalta
We show that for C*-algebras with the Global Glimm Property, the rank of every operator can be realized as the rank of a soft operator, that is, an element whose hereditary sub-C*-…
Fraïssé Theory for Cuntz semigroups
Laurent Cantier, Eduard Vilalta
We introduce a Fraïssé theory for abstract Cuntz semigroups akin to the theory of Fraïssé categories developed by Kubiś. In particular, we show that any (Cuntz) Fraïssé category ha…
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…
Nowhere scattered multiplier algebras
Eduard Vilalta
We study sufficient conditions under which a nowhere scattered C*-algebra has a nowhere scattered multiplier algebra , that is, we study when h…
Soft operators in C*-algebras
Hannes Thiel, Eduard Vilalta
We say that a C*-algebra is soft if it has no nonzero unital quotients, and we connect this property to the Hjelmborg-Rørdam condition for stability and to property (S) of Ortega-P…
The Global Glimm Property
Hannes Thiel, Eduard Vilalta
It is known that a C*-algebra with the Global Glimm Property is nowhere scattered (it has no elementary ideal-quotients), and the Global Glimm Problem asks if the converse holds. W…
Nowhere scattered C*-algebras
Hannes Thiel, Eduard Vilalta
We say that a C*-algebra is nowhere scattered if none of its quotients contains a minimal open projection. We characterize this property in various ways, by topological properties…
The Cuntz semigroup of unital commutative AI-algebras
Eduard Vilalta
We provide an abstract characterization for the Cuntz semigroup of unital commutative AI-algebras, as well as a characterization for abstract Cuntz semigroups of the form $\text{Ls…
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…
A local characterization for the Cuntz semigroup of AI-algebras
Eduard Vilalta
We give a local characterization for the Cuntz semigroup of AI-algebras building upon Shen's characterization of dimension groups. Using this result, we provide an abstract charact…
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…