We compute the nuclear dimension of separable, simple, unital, nuclear, Z Z-stable C^* C∗-
algebras. This makes classification accessible from Z Z-stability and in particular brings …

Starting from Kirchberg's theorems announced at the operator algebra conference in
Geneve in 1994, namely O2⊗ A∼= O2 for separable unital nuclear simple A and O∞⊗ A∼ …

We construct a unital separable C*-algebra Z as an analog of the hyperfinite type II 1 factor.
Besides being nuclear, simple, projectionless, and infinite-dimensional, Z has a unique …

A classification is given of certain separable nuclear C*-algebras of real rank zero and
stable rank one. Theses termes refer to density of the invertible elements within the sets of …

Around 1990 George Elliott proposed a bold conjecture that a certain subcategory c of
separable nuclear C∗-algebras could be classified by K-theoretic invariants Ell which …

The techniques of universal algebra are applied to the category of C*-algebras. An important
difference, central to this book, is that one can consider approximate representations of …

A classification is given of what may turn out to be all separable nuclear simple C*-algebras
of real rank zero and stable rank one.(These terms refer to density of the invertible elements …

We introduce the concept of finitely coloured equivalence for unital $^* $-homomorphisms
between $\mathrm C^* $-algebras, for which unitary equivalence is the $1 $-coloured case …

We give a number of new characterizations of the Jiang–Su algebra 𝒵, both intrinsic and
extrinsic, in terms of C*-algebraic, dynamical, topological and K-theoretic conditions. Along …

Provides the fundamentals of representations of finitely presented*-algebras by bounded
operators. The theory is illustrated with numerous examples of*-algebra. The examples, in …