Related papers: Comparison theory and smooth minimal C*-dynamics

Let $\Omega$ be a compact subset of $\mathbb{C}$ and let $A$ be a unital simple, separable $C^*$-algebra with stable rank one, real rank zero and strict comparison. We show that, given a Cu-morphism $\alpha:{\rm Cu}(C(\Omega))\to {\rm…

Based on the projective matrix spaces studied by B. Schwarz and A. Zaks, we study the notion of projective space associated to a C*-algebra A with a fixed projection p. The resulting space P(p) admits a rich geometrical structure as a…

We consider three notions of divisibility in the Cuntz semigroup of a C*-algebra, and show how they reflect properties of the C*-algebra. We develop methods to construct (simple and non-simple) C*-algebras with specific divisibility…

This paper is aimed at investigating links between Fell bundles over Morita equivalent groupoids and their corresponding reduced C*-algebras. Mainly, we review the notion of Fell pairs over a Morita equivalence of groupoids, and give the…

According to J. Feldman and C. Moore's well-known theorem on Cartan subalgebras, a variant of the group measure space construction gives an equivalence of categories between twisted countable standard measured equivalence relations and…

A class of C*-algebras is described for which the homomorphism from $C_0(0,1]$ to the algebra may be classified by means of the Cuntz semigroup functor. Examples are given of algebras--simple and non-simple--for which this classification…

We show that filtered K-theory is equivalent to a substantially smaller invariant for all real-rank-zero C*-algebras with certain primitive ideal spaces -- including the infinitely many so-called accordion spaces for which filtered K-theory…

To a large class of graphs of groups we associate a C*-algebra universal for generators and relations. We show that this C*-algebra is stably isomorphic to the crossed product induced from the action of the fundamental group of the graph of…

We show that the Dixmier-Douady theory of continuous field $C^*$-algebras with compact operators $\mathbb{K}$ as fibers extends significantly to a more general theory of fields with fibers $A\otimes \mathbb{K}$ where $A$ is a strongly…

We show that unital simple C*-algebras with tracial topological rank zero which are locally approximated by subhomogeneous C^-algebras can be classified by their ordered $K$-theory. We apply this classification result to show that certain…

For a compact group $\mathbb{G}$, the functor from unital Banach algebras with contractive morphisms to metric spaces with 1-Lipschitz maps sending a Banach algebra $A$ to the space of $\mathbb{G}$-representations in $A$ preserves filtered…

We develop a theory of type semigroups for arbitrary twisted, not necessarily Hausdorff \'etale groupoids. The type semigroup is a dynamical version of the Cuntz semigroup. We relate it to traces, ideals, pure infiniteness, and stable…

We classify unital monomorphisms into certain simple Z-stable C^*-algebras up to approximate unitary equivalence. The domain algebra C is allowed to be any unital separable commutative C^*-algebra, or any unital simple separable nuclear…

We solve a class of lifting problems involving approximate polynomial relations (soft polynomial relations). Various associated C*-algebras are therefore projective. The technical lemma we need is a new manifestation of Akemann and…

Let $B \subset A$ be a depth $2$ inclusion of simple unital $C^*$-algebras with a conditional expectation of index-finite type. We show that the second relative commutant $B' \cap A_1$ carries a canonical structure of a weak $C^*$-Hopf…

We investigate what would be a correct definition of categorical completeness for C*-categories and propose several variants of such a definition that make the category of Hilbert modules over a C*-algebra a free (co)completion. We extend…

For 0 < s < 1, let phi_s(z)=sz+(1-s). We investigate the unital C*-algebra generated by the semigroup {C_{phi_s} : 0 < s < 1} of composition operators acting on the Hardy space of the unit disk. We determine the joint approximate point…

A well-known result in dynamical systems asserts that any Cantor minimal system $(X,T)$ has a maximal rational equicontinuous factor $(Y,S)$ which is in fact an odometer, and realizes the rational subgroup of the $K_0$-group of $(X,T)$,…

We introduce a new class of C^*-algebras, which is a generalization of both graph algebras and homeomorphism C^*-algebras. This class is very large and also very tractable. We prove the so-called gauge-invariant uniqueness theorem and the…

In this paper, we prove results on the relative radius of comparison of C*-algebras and their crossed products, focusing on the non-unital setting. More precisely, let $A$ be a stably finite simple non-type-I (not necessarily unital)…