The concept of real rank of a C∗-algebra is introduced as a non-commutative analogue of
dimension. It is shown that real rank zero is equivalent to the previously defined conditions …

The theory and applications of C?-algebras are related to fields ranging from operator
theory, group representations and quantum mechanics, to non-commutative geometry and …

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 …

Inspired by a paper of S. Popa and the classification theory of nuclear $ C^* $-algebras, we
introduce a class of $ C^* $-algebras which we call tracially approximately finite dimensional …

We consider inductive limits A of sequences A 1→ A 2→⋯ finite direct sums of C∗-algebras
of continuous functions from compact Hausdorff spaces into full matrix algebras. We prove …

An alternative proof is given for the fact ([13]) that a purely infinite, simple ${C^*} $-algebra
has the FS property: the set of self-adjoint elements with finite spectrum is norm dense in the …

We first prove that every σ-unital, purely infinite, simple C∗-algebra is either unital or stable.
Consequently, purely infinite simple C∗-algebras have real rank zero. In particular, the …

In this paper, we prove a Riesz decomposition property of the local semigroup consisting of
Murray-von Neumann equivalence classes of projections in a C* gebra sé with the FS …

In this paper, we show that every separable simple tracially approximately divisible C∗ C^*‐
algebra has strict comparison, and it is either purely infinite or has stable rank one. As a …

We prove that pre-classifiable (see 3.1) simple nuclear tracially AF C*-algebras (TAF) are
classified by their K-theory. As a consequence all simple, locally AH and TAF C*-algebras …