Related papers: Persistence approximation property and controlled …

Approximate Bayesian Computation (ABC for short) is a family of computational techniques which offer an almost automated solution in situations where evaluation of the posterior likelihood is computationally prohibitive, or whenever…

We prove implications among the conditions in the title for an inclusion of a C*-algebra A in a C*-algebra B, and we also relate this to several other properties in case B is a crossed product for an action of a group, inverse semigroup or…

We introduce a new class of C^*-algebras, which is a generalization of both graph algebras and homeomorphism C^*-algebras. This class is very large and also very tractable. We prove the so-called gauge-invariant uniqueness theorem and the…

We provide a new computation of the K-theory of the group $C^*$-algebra of the solvable Baumslag-Solitar group $BS(1,n)\;(n\neq 1)$; our computation is based on the Pimsner-Voiculescu 6-terms exact sequence, by viewing $BS(1,n)$ as a…

We establish the dual equivalence of the category of (potentially nonunital) operator systems and the category of pointed compact nc (noncommutative) convex sets, extending a result of Davidson and the first author. We then apply this dual…

This work is intended to present the basic properties of $KO$-theory for real $C^*$-algebras and to explain its relationship with complex $K$-theory and with $KR$- theory. Whenever possible we will rely upon proofs in printed literature,…

We investigate $C^*$-algebras associated with row-finite topological higher-rank graphs with no source, which are based on product system $C^*$-algebras. We prove the Cuntz-Krieger uniqueness theorem, and provide the condition of simplicity…

We provide a Cuntz-Pimsner model for graph of groups $C^*$-algebras. This allows us to compute the $K$-theory of a range of examples and show that graph of groups $C^*$-algebras can be realised as Exel-Pardo algebras. We also make a…

Given C$^*$-algebras $A$ and $B$ and a $^*$-homomorphism $\phi:A\rightarrow B$, we adopt the portrait of the relative $K$-theory $K_*(\phi)$ due to Karoubi using Banach categories and Banach functors. We show that the elements of the…

We show that certain C*-algebras which have been studied among others by Arzumanian, Vershik, Deaconu, and Renault in connection to a measure preserving transformation of a measure space and/or to a covering map of a compact space are…

A discrete group is said to be C*-simple if its reduced C*-algebra is simple, and is said to have the unique trace property if its reduced C*-algebra has a unique tracial state. A dynamical characterization of C*-simplicity was recently…

We present an axiomatic frame (in Prt I of this book) in which many results of the K-theory for C*-algebras are proved. Then we construct an example for this axiomatic theory (in Part II), which generalizes the classical theory for…

In this paper we generalize the notion of Cuntz-Pimsner algebras of $C^*$-correspondences to the setting of subproduct systems. The construction is justified in several ways, including the Morita equivalence of the operator algebras under…

We prove a relative analogue of equivalence between nuclearity and CPAP. In its proof, the notion of weak containment for C$^*$-correspondences plays an important role. As an application we prove $KK$-equivalence between full and reduced…

In this paper, we introduce the countable chain condition for C*-algebras and study its fundamental properties. We show independence from ZFC of the statement that this condition is preserved under the tensor products of C*-algebras.

We introduce a property of C*-correspondences, which we call Condition (S), to serve as an analogue of Condition (L) of graphs. We use Condition (S) to prove a Cuntz-Krieger Uniqueness Theorem for Cuntz-Pimsner algebras and obtain…

We prove a noncommutative variant of Saskin's classical theorem -- on the connection between Choquet boundaries for function spaces and Korovkin sets -- for operator systems generating separable Type I C*-algebras. The main result implies…

We examine crossed product C*-algebras associated with non-minimal free actions of countably infinite discrete abelian groups on the circle, extending the work of Putnam, Schmidt, and Skau. We obtain a large class of unital separable…

For a directed graph $E$, we compute the $K$-theory of the $C^*$-algebra $C^*(E)$ from the Cuntz-Krieger generators and relations. First we compute the $K$-theory of the crossed product $C^*(E)\times_\gamma\IT$, and then using duality and…

We give a new definition for the crossed-product of a C*-algebra A by a *-endomorphism \alpha, which depends not only on the pair (A,\alpha) but also on the choice of a transfer operator (defined in the paper). With this we generalize some…