We prove that if a conditional expectation from a simple CÃ-algebra onto its CÃ-subalgebra
satisfies the Pimsner-Popa inequality, there exists a quasi-basis. As an application, we …

The Corona Factorization Property, originally invented to study extensions of C*-algebras,
conveys essential information about the intrinsic structure of the C*-algebra. We show that …

We show that the homotopy groups of the group of quasi-unitaries in C*-algebras form a
homology theory on the category of all C*-algebras which becomes topological K-theory …

We give a detailed introduction to the theory of Cuntz semigroups for C*-algebras.
Beginning with the most basic definitions and technical lemmas, we present several results …

We prove that the category of abstract Cuntz semigroups is bicomplete. As a consequence,
the category admits products and ultraproducts. We further show that the scaled Cuntz …

The class of C*-algebras, that arise as the crossed product of a stable simple AF-algebra
with a Z-action determined by an automorphism, which maps a projection in the algebra …

We classify finite group actions on some classes of C∗-algebras with the Rohlin property in
terms of the K-groups. A group cohomological obstruction is obtained for the K-groups of a …

The first named author has given a classification of all separable, nuclear C*-algebras A that
absorb the Cuntz algebra O∞.(We say that A absorbs O∞ if A is isomorphic to A⊗ O∞.) …

We exhibit a countably infinite family of simple, separable, nuclear, and mutually non-
isomorphic C $^* $-algebras which agree on $\mathrm {K} $-theory and traces. The …

We present a uniqueness theorem for k-graph C⁎-algebras that requires neither an
aperiodicity nor a gauge invariance assumption. Specifically, we prove that for the injectivity …