A category is described to which the Cuntz semigroup belongs and as a functor into which it preserves inductive limits. 1. Recently, Toms in [26] used the refinement of the invariant K0 introduced by… (More)

A common generalization is given of what are often referred to as the Weyl–von Neumann theorems of Voiculescu, Kasparov, Kirchberg, and, more recently, Lin. (These in turn extend a result of Brown,… (More)

It is shown that, for a C*-algebra of stable rank one (i.e., in which the invertible elements are dense), two well-known isomorphism invari-ants, the Cuntz semigroup and the Thomsen semigroup,… (More)

We prove that all unital separable continuous fields of C*-algebras over [0, 1] with fibers isomorphic to the Cuntz algebra On (2 ≤ n ≤ ∞) are trivial. More generally, we show that if A is a… (More)

Let X be an infinite compact metrizable space, and let σ : X → X be a minimal homeomorphism. Suppose that (X,σ) has zero mean topological dimension. The associated C*algebra A = C(X) oσ Z is shown to… (More)

We report on recent progress in the program to classify separable amenable C∗-algebras. Our emphasis is on the newly apparent role of regularity properties such as finite decomposition rank, strict… (More)

T HE FREQUENCY of arteriosclerosis (intimal thickening with or withont lipid deposits) in mammals and birds of the Philadelphia Zoological Garden has increased 10fold since 1935.1 This inerease has… (More)

ut Uj = (exp — 27110^) Uj ut for 1 ^ / <j ^ «, where the 6tj are real numbers. This algebra was called in [3,4,5] the noncommutative n-torus. It is closely related to the irreducible representations… (More)

We show that in the generic case the smooth noncommutative tori associated to two n×n real skew-symmetric matrices are Morita equivalent if and only if the matrices are in the same orbit of the… (More)

A large class of simple stably projectionless C*-algebras are shown to arise as crossed products of simple purely infinite C*-algebras by trace scaling one-parameter automorphism groups. The Elliott… (More)