Related papers: A similarity degree characterization of nuclear $C…

We show that every nuclear $\mathcal O_\infty$-stable *-homomorphism with a separable exact domain has nuclear dimension at most 1. In particular separable, nuclear, $\mathcal O_\infty$-stable C*-algebras have nuclear dimension 1. We also…

Let H be a compact quantum group with faithful Haar measure and bounded counit. If H acts on a C*-algebra A, we show that A is nuclear if and only if its fixed-point subalgebra is nuclear. As a consequence H is a nuclear C*-algebra.

We show that if X is a finite dimensional locally compact Hausdorff space, then the crossed product of C_0(X) by any automorphism has finite nuclear dimension. This generalizes previous results, in which the automorphism was required to be…

We prove that a discrete group $G$ is amenable iff it is strongly unitarizable in the following sense: every unitarizable representation $\pi$ on $G$ can be unitarized by an invertible chosen in the von Neumann algebra generated by the…

If A is a C*-algebra, G a locally compact group, K{\subset}G a compact subgroup and {\alpha}:G{\to}Aut(A) a continuous homomorphism, let Ax_{{\alpha}}G denote the crossed product. In this paper we prove that Ax_{{\alpha}}G is nuclear…

We show that separable, nuclear and strongly purely infinite C*-algebras have finite nuclear dimension. In fact, the value is at most three. This exploits a deep structural result of Kirchberg and R{\o}rdam on strongly purely infinite…

Consider a graph C*-algebra C*(E) with a purely infinite ideal I (possibly all of C*(E)) such that I has only finitely many ideals and C*(E)/I is approximately finite dimensional. We prove that the nuclear dimension of C*(E) is 1. If I has…

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 study the local operator space structure of nuclear $C^*$-algebras. It is shown that a $C^*$-algebra is nuclear if and only if it is an $\OL_{\infty, \la}$ space for some (and actually for every) $\la > 6$. The $\OL_\infty$ constant…

Starting from Kirchberg's theorems announced in 1994, namely O_2 tensor A is isomorphic to O_2 for separable unital nuclear simple A and O_infinity tensor A is isomorphic to A if in addition A is purely infinite, we prove that…

We prove that Z-stable, simple, separable, nuclear, non-unital C*-algebras have nuclear dimension at most 1. This completes the equivalence between finite nuclear dimension and Z-stability for simple, separable, nuclear, non-elementary…

It is shown that if a C*-algebra has nuclear dimension $n$ then its Cuntz semigroup has the property of $n$-comparison. It then follows from results by Ortega, Perera, and Rordam that $\sigma$-unital C*-algebras of finite nuclear dimension…

We introduce the concept of finitely coloured equivalence for unital *-homomorphisms between C*-algebras, for which unitary equivalence is the 1-coloured case. We use this notion to classify *-homomorphisms from separable, unital, nuclear…

Suppose that $\mathcal M$ is a countably decomposable type II$_1$ von Neumann algebra and $\mathcal A$ is a separable, non-nuclear, unital C$^*$-algebra. We show that, if $\mathcal M$ has Property $\Gamma$, then the similarity degree of…

We show that the tensor product of two unital C*-algebras, one of which is nuclear and admits a unital *-homomorphism from (the building blocks of) the Jiang-Su algebra, has Kadison's similarity property. As a consequence, we obtain that a…

We obtain an improved upper bound for the nuclear dimension of extensions of $\mathcal{O}_\infty$-stable $\rm{C}^*$-algebras. In particular, we prove that the nuclear dimension of a full extension of an $\mathcal{O}_\infty$-stable…

The main result here is that a simple separable C*-algebra is Z-stable (where Z denotes the Jiang-Su algebra) if (i) it has finite nuclear dimension or (ii) it is approximately subhomogeneous with slow dimension growth. This generalizes the…

Let $A$ be a unital operator algebra. Let us assume that every {\it bounded\/} unital homomorphism $u\colon \ A\to B(H)$ is similar to a {\it contractive\/} one. Let $\text{\rm Sim}(u) = \inf\{\|S\|\, \|S^{-1}\|\}$ where the infimum runs…

Nuclear $C^*$-algebras having a system of completely positive approximations formed with convex combinations of a uniformly bounded number of order zero summands are shown to be approximately finite dimensional.

It is shown that if $A$ and $B$ are unital separable simple nuclear $\mathcal Z$-stable C$^*$-algebras and there is a unital embedding $A \rightarrow B$ which is invertible on $KK$-theory and traces, then $A \cong B$. In particular, two…