Related papers: The Blackadar-Handelman theorem for non-unital C*-…

We study the validity of the Blackadar-Kirchberg conjecture for extensions of separable, nuclear, quasidiagonal $C^*$-algebras that satisfy the UCT. More specifically, we show that the conjecture for the extension has an affirmative answer…

We give a complete description of which unital graph C*-algebras are semiprojective, and use it to disprove two conjectures by Blackadar. To do so, we perform a detailed analysis of which projections are properly infinite in such…

We define and study large and stably large subalgebras of simple unital C*-algebras. The basic example is the orbit breaking subalgebra of a crossed product by Z, as follows. Let X be an infinite compact metric space, let h be a minimal…

It is shown that a unital C*-algebra A has the Dixmier property if and only if it is weakly central and satisfies certain tracial conditions. This generalises the Haagerup-Zsido theorem for simple C*-algebras. We also study a uniform…

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 of historical importance, such as Cuntz's theorem on the existence…

It is shown that all 2-quasitraces on a unital exact C*-algebra are traces. As consequences one gets: (1) Every stably finite exact unital C*-algebra has a tracial state, and (2) if an AW*-factor of type II_1 is generated (as an…

We prove some stability results for certain classes of C*-algebras. We prove that whenever $A$ is a finite-dimensional C*-algebra, $B$ is a C*-algebra and $\phi\colon A\to B$ is approximately a $^*$-homomorphism then there is an actual…

In the paper, we give two new characterizations of separable inner quasidiagonal C*-algebras. Base on these characterizations, we show that a unital full free product of two inner quasidiagonal C*-algebras is inner quasidiagonal again. As…

We conjecture that a unital C$^*$-algebra is a W$^*$-algebra if and only if each of its maximal abelian self-adjoint subalgebras is a W$^*$-algebra; this is a space-free analogue of a known result due to G.K. Pedersen. Our main result is a…

Using Cuntz semigroup techniques, we characterize when limit traces are dense in the space of all traces on a free ultrapower of a C*-algebra. More generally, we consider density of limit quasitraces on ultraproducts of C*-algebras. Quite…

We show that a simple separable unital nuclear nonelementary $C^*$-algebra whose tracial state space has a compact extreme boundary with finite covering dimension admits uniformly tracially large order zero maps from matrix algebras into…

We present a stable uniqueness theorem for non-unital C*-algebras. Generalized tracial rank one is defined for stably projectionless simple C*-algebras. Let $A$ and $B$ be two stably projectionless separable simple amenable C*-algebras with…

In this paper we study stable finiteness of ample groupoid algebras with applications to inverse semigroup algebras and Leavitt path algebras, recovering old results and proving some new ones. In addition, we develop a theory of (faithful)…

We investigate the closed convex hull of unitary orbits of selfadjoint elements in arbitrary unital C*-algebras. Using a notion of majorization against unbounded traces, a characterization of these closed convex hulls is obtained.…

We investigate the set of maximally mixed states of a C*-algebra, extending previous work by Alberti on von Neumann algebras. We show that, unlike for von Neumann algebras, the set of maximally mixed states of a C*-algebra may fail to be…

We prove that the C*-algebra of a minimal diffeomorphism satisfies Blackadar's Fundamental Comparability Property for positive elements. This leads to the classification, in terms of K-theory and traces, of the isomorphism classes of…

We study the uniform property $\Gamma$ for separable simple $C^*$-algebras which have quasitraces and may not be exact. We show that a stably finite separable simple $C^*$-algebra $A$ with strict comparison and uniform property $\Gamma$ has…

We prove that if A is a \sigma-unital exact C*-algebra of real rank zero, then every state on K_0(A) is induced by a 2-quasitrace on A. This yields a generalisation of Rainone's work on pure infiniteness and stable finiteness of crossed…

We prove that von Neumann algebras and separable nuclear $C^*$-algebras are stable for the Banach-Mazur cb-distance. A technical step is to show that unital almost completely isometric maps between $C^*$-algebras are almost multiplicative…

We construct a unital pre-C*-algebra $A_0$ which is stably finite, in the sense that every left invertible square matrix over $A_0$ is right invertible, while the C*-completion of $A_0$ contains a non-unitary isometry, and so it is…