Related papers: Tracial approximation in simple C*-algebras

We give new characterizations to ensure that a free product of groups with amalgamation has a simple reduced group C*-algebra, and provide a concrete example of an amalgam with trivial kernel, such that its reduced group C*-algebra has a…

Let $A$ be a separable simple exact ${\cal Z}$-stable $C^*$-algebra. We show that the unitay group of ${\tilde A}$ has the cancellation property. If $A$ has continuous scale, the Cuntz semigroup of $\tilde A$ has the strict comparison…

We prove that a factorial tracially complete C*-algebra with CPoU has real rank zero and stable rank one. This leads to an essentially complete description of the Cuntz semigroup of these algebras. In particular, the results of this paper…

Let $A$ be a unital simple separable C*-algebra satisfying the UCT. Assume that $\mathrm{dr}(A)<+\infty$, $A$ is Jiang-Su stable, and $\mathrm{K}_0(A)\otimes \mathbb{Q}\cong \mathbb{Q}$. Then $A$ is an ASH algebra (indeed, $A$ is a…

We examine crossed product C*-algebras associated with non-minimal free actions of countably infinite discrete abelian groups on the circle, extending the work of Putnam, Schmidt, and Skau. We obtain a large class of unital separable…

Let $X$ be a compact metric space, let $A$ be a unital AH algebra with large matrix sizes, and let $B$ be a stably finite unital C*-algebra. Then we give a lower bound for the radius of comparison of $C(X) \otimes B$ and prove that the…

We consider inductive systems of C*-algebras with completely positive contractive connecting maps. We define a condition, called C*-encoding, which is sufficient for the limit of the system to be completely order isomorphic to a C*-algebra…

We show that if B is a C*-subalgebra of a C*-algebra A such that B contains a bounded approximate identity for A, and if L is the pull-back to A of the quotient norm on A/B, then L is strongly Leibniz. In connection with this situation we…

A complete contraction on a C*-algebra A, which preserves all closed two sided ideals J, can be approximated pointwise by elementary complete contractions if and only if the induced map on the tensor product of B with A/J is contractive for…

We introduce diagonal comparison, a regularity property of diagonal pairs where the sub-C*-algebra has totally disconnected spectrum, and establish its equivalence with the concurrence of strict comparison of the ambient C*-algebra and…

Let $G$ be a countable abelian group. We construct a unital simple projectionless C*-algebra $A$ with a unique tracial state, that satisfies $(K_0(A), [1_A]) \cong (\Z, 1) $, $K_1(A) \cong G$, absorbs the Jiang-Su algebra tensorially, and…

Following Robert's [26], we study the structure of unitary groups and groups of approximately inner automorphisms of unital $C^*$-algebras, taking advantage of the former being Banach-Lie groups. For a given unital $C^*$-algebra $A$, we…

We study a pair of $C^*$-algebras by associating a $*$-homomorphism from $A$ to $B$ allowing an approximate left-inverse to the sequence algebra of $A$ in a manner reminiscent of several tracial approximation properties. We are particularly…

It is shown that all 2-quasitraces on a unital exact C*-algebra are traces. As consequences one gets: (1) Every stably finite exact unital C*-algebra has a tracial state, and (2) if an AW*-factor of type II_1 is generated (as an…

Building on previous work of Kadison--Ringrose, Elliott, Akemann--Pedersen, and this author, we prove a dichotomy for the relation of outer equivalence of derivations and unitary equivalence of derivable automorphisms for a separable…

We observe that a recent theorem of Sato, Toms-White-Winter and Kirchberg-Rordam also holds for certain nonunital C*-algebras. Namely, we show that an algebraically simple, separable, nuclear, nonelementary C*-algebra with strict…

Given a simple, acyclic dimension group $G_{0}$ and countable, torsion-free, abelian group $G_{1}$, we construct a minimal, amenable, \'{e}tale equivalence relation $R$ on a Cantor set whose associated groupoid $C^{*}$-algebra, $C^{*}(R)$,…

Let $C$ be a unital AH-algebra and let $A$ be a unital separable simple \CA with tracial rank zero. Suppose that $\phi_1, \phi_2: C\to A$ are two unital monomorphisms. We show that there is a continuous path of unitaries $\{u_t: t\in [0,…

It is proved that classifiable simple separable nuclear purely infinite C*-algebras having finitely generated K-theory and torsion-free K_1 are semiprojective. This is accomplished by exhibiting these algebras as C*-algebras of infinite…

We construct an example of a simple approximately homogeneous C*-algebra such that its Elliott invariant admits an automorphism which is not induced by an automorphism of the algebra.