Related papers: Approximately Multiplicative Decompositions of Nuc…

Nuclear C*-algebras enjoy a number of approximation properties, most famously the completely positive approximation property. This was recently sharpened to arrange for the incoming maps to be sums of order-zero maps. We show that, in…

We show that nuclear C*-algebras have a refined version of the completely positive approximation property, in which the maps that approximately factorize through finite dimensional algebras are convex combinations of order zero maps. We use…

We introduce the decomposition rank, a notion of covering dimension for nuclear C^*-algebras. The decomposition rank generalizes ordinary covering dimension and has nice permanence properties; in particular, it behaves well with respect to…

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.

The subject of quasidiagonality is of much interest in many places - among other things, in the classification program for simple unital separable nuclear C*-algebras. In this note, we give two characterizations of nuclearity and…

We consider 2-positive almost order zero (disjointness preserving) maps on C*-algebras. Generalizing the argument of M. Choi for multiplicative domains, we give an internal characterization of almost order zero for 2-positive maps. It is…

I give an overview of recent developments in the structure and classification theory of separable, simple, nuclear C*-algebras. I will in particular focus on the role of quasidiagonality and amenability for classification, and on the…

In this paper, we show that a completely positive linear map is weakly nuclear if and only if its complexification is weakly nuclear. It is shown that a real $C^*$-algebra is exact if and only if its complexification is exact and similar…

The completely positive rank is an analogue of topological covering dimension, defined for nuclear C*-algebras via completely positive approximations. These may be thought of as simplicial approximations of the algebra, which leads to the…

We show that the strengthened version of the completely positive approximation property of Brown, Carri\'on, and White---where the downward maps are asymptotically order zero and the upward maps are convex combinations of order zero…

We write arbitrary separable nuclear C*-algebras as limits of inductive systems of finite-dimensional C*-algebras with completely positive connecting maps. The characteristic feature of such CPC*-systems is that the maps become more and…

A problem of completing a linear map on C*-algebras to a completely positive map is analyzed. It is shown that whenever such a completion is feasible there exists a unique minimal completion. This theorem is used to show that under some…

We construct a class of positive linear maps on matrix algebras. We find conditions when these maps are atomic, decomposable and completely positive. We obtain a large class of atomic positive linear maps. As applications in quantum…

We demonstrate the existence of quasiconformal mappings on closed manifolds that cannot be decomposed as a composition of mappings with arbitrarily small conformal distortion.

We prove that faithful traces on separable and nuclear C*-algebras in the UCT class are quasidiagonal. This has a number of consequences. Firstly, by results of many hands, the classification of unital, separable, simple and nuclear…

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 investigate $^*$-homomorphisms with nuclear dimension equal to zero. In the framework of classification of $^*$-homo-morphisms, we characterise such maps as those that can be approximately factorised through an AF-algebra. Along the way,…

In this paper, we study the problem of approximately computing the product of two real matrices. In particular, we analyze a dimensionality-reduction-based approximation algorithm due to Sarlos [1], introducing the notion of nuclear rank as…

We compute the nuclear dimension of separable, simple, unital, nuclear, Z-stable C*-algebras. This makes classification accessible from Z-stability and in particular brings large classes of C*-algebras associated to free and minimal actions…

Structural approximations to positive, but not completely positive maps are approximate physical realizations of these non-physical maps. They find applications in the design of direct entanglement detection methods. We show that many of…