Related papers: Boundary rigidity for free product C*-algebras

Let A be a unital separable simple infinite-dimensional nuclear C*-algebra with at least one tracial state. We prove that if the trace space of A has compact finite-dimensional extreme boundary then there exist unital embeddings of matrix…

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…

Finiteness conditions for $C^*$-algebras like AF-embeddability, quasidiagonality, stable finiteness have been studied by many authors and shown to be equivalent for certain classes of $C^*$-algebras. For example, Schfhauser proves that…

In the paper, we consider the question whether a unital full amalgamated free product of quasidiagonal C*-algebras is quasidiagonal again. We give a sufficient condition such that a unital full amalgamated free product of quasidiagonal…

We construct a generalized version for the free product of unital C*-algebras over a family of unital C*-subalgebras, starting from the group-analogue. When all the subalgebras are the same, we recover the free product with amalgamation…

Let H be a full Hilbert bimodule over a C*-algebra A. We show that the Cuntz-Pimsner C*-algebra associated to H is exact if and only if A is exact. Using this result, we give alternative proofs for exactness of reduced amalgamated free…

Let $I$ be any nonempty set and $(M_i, \varphi_i)_{i \in I}$ any family of nonamenable factors, endowed with arbitrary faithful normal states, that belong to a large class $\mathcal C_{\rm anti-free}$ of (possibly type III) von Neumann…

We prove that unital graph C*-algebras often admit a convenient decomposition into amalgamated free products. We use this to give a complete characterization of when a unital graph C*-algebra is residually finite-dimensional and when it is…

This paper studies direct limits of full upper triangular matrix algebras with embeddings which are not *-extendible. A representation of the limit algebra is found so that the generated C*-algebra is the C*-envelope. Some examples are…

We give various characterizations of into (not necessarily onto) complete isometries between $C^*$-algebras, generalizing a classical result of Holsztynski. Our results are related to a natural embedding of the noncommutative Shilov…

Consider the reduced free product of C*-algebras, (A,\phi)=(A_1,\phi_1)*(A_2,\phi_2), with respect to states \phi_1 and \phi_2 that are faithful. If \phi_1 and \phi_2 are traces, if the so-called Avitzour conditions are satisfied, (i.e. A_1…

Let X be a path connected, compact metric space and let A be a unital separable simple nuclear Z-stable real rank zero C*-algebra. We classify all the unital *-embeddings (up to approximate unitary equivalence) of C(X) into A. Specifically,…

We consider representations of the free group $F_2$ on two generators such that the norm of the sum of the generators and their inverses is bounded by $\mu\in[0,4]$. These $\mu$-constrained representations determine a C*-algebra $A_{\mu}$…

Let C be a separable unital C*-algebra, not isomorphic to the complex numbers, equipped with a faithful tracial state. Let A be a unital direct limit of one dimensional NCCW complexes, also equipped with a faithful tracial state. Suppose…

Every $\mathrm{C}^*$-algebra, regardless of its density character, can be embedded into the Calkin algebra in a forcing extension of the universe obtained without collapsing any cardinal.

We compute the K-theory for C*-algebras naturally associated with rings of integers in number fields. The main ingredient is a duality theorem for arbitrary global fields. It allows us to identify the crossed product arising from affine…

Let $X$ be a compact metric space, let $A$ be a unital AH algebra with large matrix sizes, and let $B$ be a stably finite unital C*-algebra. Then we give a lower bound for the radius of comparison of $C(X) \otimes B$ and prove that the…

Let $\Delta$ be an infinite, locally finite tree with more than two ends. Let $\Gamma<\aut(\Delta)$ be an acylindrical uniform lattice. Then the boundary algebra $\cl A_\Gamma = C(\partial\Delta)\rtimes \Gamma$ is a simple Cuntz-Krieger…

We consider separable $C^*$-dynamical systems $(A,G,\alpha)$ for which the induced action of the group $G$ on the spectrum $\hat A$ of the $C^*$-algebra $A$ is free. We study how the representation theory of the associated crossed-product…

We prove a strong classification result for a certain class of $C^{*}$-algebras with primitive ideal space $\widetilde{\mathbb{N}}$, where $\widetilde{\mathbb{N}}$ is the one-point compactification of $\mathbb{N}$. This class contains the…