Related papers: Approximation property of $C^*$-algebraic Bundles

We extend applications of Furstenberg boundary theory to the study of $C^*$-algebras associated to minimal actions $\Gamma\!\curvearrowright\! X$ of discrete groups $\Gamma$ on locally compact spaces $X$. We introduce boundary maps on…

In this article we use semigroupoids to describe a notion of algebraic bundles, mostly motivated by Fell ($C^*$-algebraic) bundles, and the sectional algebras associated to them. As the main motivational example, Steinberg algebras may be…

We propose a new framework that generalizes the parameters of neural network models to $C^*$-algebra-valued ones. $C^*$-algebra is a generalization of the space of complex numbers. A typical example is the space of continuous functions on a…

Given a normal subgroup bundle $\mathcal A$ of the isotropy bundle of a groupoid $\Sigma$, we obtain a twisted action of the quotient groupoid $\Sigma/\mathcal A$ on the bundle of group $C^*$-algebras determined by $\mathcal A$ whose…

We survey the results required to pass between full and reduced coactions of locally compact groups on C*-algebras, which say, roughly speaking, that one can always do so without changing the crossed-product C*-algebra. Wherever possible we…

We present a $C^*$-algebra which is naturally associated to the $ax+b$-semigroup over $\mathbb N$. It is simple and purely infinite and can be obtained from the algebra considered by Bost and Connes by adding one unitary generator which…

In this note we start the study of whether the reduced C*-algebra of an inverse semigroup is quasi-diagonal, making explicit use of the inner structure of this class of semigroups in order to produce quasi-diagonal approximations. Given a…

We introduce a graph theoretic property called Condition (N) for finitely separated graphs and prove that it is equivalent to both nuclearity and exactness of the associated universal tame graph C*-algebra.

We give a rigorous account and prove continuity properties for the correspondence between almost flat bundles on a triangularizable compact connected space and the quasi-representations of its fundamental group. For a discrete countable…

We introduce the nuclear dimension of a C*-algebra; this is a noncommutative version of topological covering dimension based on a modification of the earlier concept of decomposition rank. Our notion behaves well with respect to inductive…

We describe the envelope C*-algebra associated to a partial action of a countable discrete group on a locally compact space as a groupoid C*-algebra (more precisely as a C*-algebra from an equivalence relation) and we use our approach to…

We introduce a cohomological invariant arising from a class in nonabelian cohomology. This invariant generalizes the Dixmier-Douady class and encodes the obstruction to a C*-algebra bundle being the fixed-point algebra of a gauge action. As…

For an action of a finite group on a C*-algebra, we present some conditions under which properties of the C*-algebra pass to the crossed product or the fixed point algebra. We mostly consider the ideal property, the projection property,…

We introduce a notion of ellipticity of complexes of linear pseudodifferential operators acting on sections of $A$-Hilbert bundles over smooth manifolds, $A$ being a $C^*$-algebra. We prove that the cohomology groups of an $A$-elliptic…

The CBH theorem characterises quantum theory within a C*-algebraic framework. Namely, mathematical properties of C*-algebras modelling quantum systems are equivalent to constraints that are information-theoretic in nature: (1)…

Let $X$ be compact Hausdorff, and $\phi: X \to X$ a continuous surjection. Let $\mathcal{A}$ be the semicrossed product algebra corresponding to the relation $fU = Uf\circ \phi$. Then the C$^*$-envelope of $\mathcal{A}$ is the crossed…

We study the Haagerup property for C*-algebras. We first give new examples of C*-algebras with the Haagerup property. A nuclear C*-algebra with a faithful tracial state always has the Haagerup property, and the permanence of the Haagerup…

We show that a separable C*-algebra is an inductive limits of projective C*-algebras if and only if it has trivial shape, that is, if it is shape equivalent to the zero C*-algebra. In particular, every contractible C*-algebra is an…

We study the $C^*$-algebras associated to upper-semicontinuous Fell bundles over second-countable Hausdorff groupoids. Based on ideas going back to the Packer--Raeburn "Stabilization Trick," we construct from each such bundle a groupoid…

The residual finite-dimensionality of a $\mathrm{C}^*$-algebra is known to be encoded in a topological property of its space of representations, stating that finite-dimensional representations should be dense therein. We extend this…