Related papers: Strict comparison in reduced group $C^*$-algebras

We study the Haagerup property for C*-algebras. We first give new examples of C*-algebras with the Haagerup property. A nuclear C*-algebra with a faithful tracial state always has the Haagerup property, and the permanence of the Haagerup…

Given a commensurated subgroup $\Lambda$ of a group $\Gamma$, we completely characterize when the inclusion $\Lambda\leq \Gamma$ is $C^*$-irreducible and provide new examples of such inclusions. In particular, we obtain that…

We consider inductive systems of C*-algebras with completely positive contractive connecting maps. We define a condition, called C*-encoding, which is sufficient for the limit of the system to be completely order isomorphic to a C*-algebra…

We study several notions of shift equivalence for C*-correspondences and the effect that these equivalences have on the corresponding Pimsner dilations. Among others, we prove that non-degenerate, regular, full C*-correspondences which are…

For any reduced free product $\mathrm{C}^*$-algebra $(A, \varphi) =(A_1, \varphi_1) \star (A_2, \varphi_2)$, we prove a boundary rigidity result for the embedding of $A$ into its associated $\mathrm{C}^*$-algebra $\Delta \mathbf{T}(A,…

Our purpose is to study in the setting of locally compact groupoids the analogues of the well-known equivalent definitions of exactness for discrete groups. Our best results are obtained for a class of \'etale groupoids that we call inner…

In his work on the Novikov conjecture, Yu introduced Property $A$ as a readily verified criterion implying coarse embeddability. Studied subsequently as a property in its own right, Property $A$ for a discrete group is known to be…

Cuntz algebra $\mathcal O_2$ is the universal $C^*$-algebra generated by two isometries $s_1, s_2$ satisfying $s_1s_1^*+s_2s_2^*=1$. This is separable, simple, infinite $C^*$-algebra containing a copy of any nuclear $C^*$-algebra. The…

It is shown in this paper that two positive elements of a C*-algebra agree on all lower semicontinuous traces if and only if they are equivalent in the sense of Cuntz and Pedersen. A similar result is also obtained in the more general case…

A necessary and sufficient condition for the simplicity of the C*-algebra reduced free product of finite dimensional abelian algebras is found, and it is proved that the stable rank of every such free product is 1. Related results about…

A group $G$ is called $W^*$-superrigid (resp. $C^*$-superrigid) if it is completely recognizable from its von Neumann algebra $L(G)$ (resp. reduced $C^*$-algebra $C_r^*(G)$). Developing new technical aspects in Popa's deformation/rigidity…

In this short note we prove that the reduced group C*-algebra of a locally compact group admits a non-zero trace if and only if the amenable radical of the group is open. This completely answers a question raised by Forrest, Spronk and…

We prove rigidity results for large classes of corona algebras, assuming the Proper Forcing Axiom. In particular, we prove that a conjecture of Coskey and Farah holds for all separable $C^*$-algebras with the metric approximation property…

Many previously studied path algebras or self-similar group algebras may be viewed as Steinberg algebras of self-similar groupoids. By way of inverse semigroup algebras, we characterize when the Steinberg algebra of a self-similar groupoid…

In this paper, we employ operator system techniques to investigate structural properties of C*-algebras. In particular, we provide more direct proofs of results concerning exactness and the local lifting property (LLP) of group…

We characterize relatively norm compact sets in the regular $C^*$-algebra of finitely generated Coxeter groups using a geometrically defined positive semigroup acting on the algebra.

We study the uniform Roe algebras associated to locally finite groups. We show that for two countable locally finite groups $\Gamma$ and $\Lambda$, the associated uniform Roe algebras $C^*_u(\Gamma)$ and $C^*_u(\Lambda)$ are $*$-isomorphic…

It is proved that every separable $C^*$-algebra of real rank zero contains an AF-sub-$C^*$-algebra such that the inclusion mapping induces an isomorphism of the ideal lattices of the two $C^*$-algebras and such that every projection in a…

Let Gamma be a discrete group satisfying the rapid decay property with respect to a length function which is conditionally negative. Then the reduced C*-algebra of Gamma has the metric approximation property. The central point of our proof…

We prove directly that if E is a directed graph in which every cycle has an entrance, then there exists a C*-algebra which is co-universal for Toeplitz-Cuntz-Krieger E-families. In particular, our proof does not invoke ideal-structure…