Related papers: Strongly self-absorbing $C^*$-algebras and Fra\"is…

We study the class of pseudocompact C*-algebras, which are the logical limits of finite-dimensional C*-algebras. The pseudocompact C*-algebras are unital, stably finite, real rank zero, stable rank one, and tracial. We show that the…

We show that if A is a simple Villadsen algebra of either the first type with seed space a finite dimensional CW complex, or of the second type, then $A$ absorbs the Jiang-Su algebra tensorially if and only if the central sequence algebra…

Building on Enders--Schemeitat--Tikuisis' classification, we show that a separable $C^*$-algebra $A$ with approximately inner flip in the UCT class is $K$-theoretically self-absorbing if and only if for every finite group $G$, the Bernoulli…

Under mild assumptions, we show that reduced free products and reduced graph products of $\mathrm{C}^\ast$-algebras are selfless in the sense of L. Robert, without assuming the rapid decay property. In particular, our main theorems yield…

We study the C*-algebra of an affine map on a compact abelian group and give necessary and sufficient conditions for strong transitivity when the group is a torus. The structure of the C*-algebra is completely determined for all strongly…

In the given article the notion of infinite norm decomposition of a C$^*$-algebra is investigated. The norm decomposition is some generalization of Peirce decomposition. It is proved that the infinite norm decomposition of any C$^*$-algebra…

In this memoir we develop a framework to study rigidity problems for Roe-like C*-algebras of countably generated coarse spaces. The main goal is to give a complete and self-contained solution to the problem of C*-rigidity for proper…

We associate reduced and full C*-algebras to arbitrary rings and study the inner structure of these ring C*-algebras. As a result, we obtain conditions for them to be purely infinite and simple. We also discuss several examples.…

Quasi *-algebras possessing a sufficient family $\mathcal{M}$ of invariant positive sesquilinear forms carry several topologies related to $\mathcal{M}$ which make every *-representation continuous. This leads to define the class of locally…

We introduce and study a natural notion of selflessness for inclusions of C*-probability spaces, which in particular implies that all intermediate C*-algebras are selfless in the sense of Robert. We identify natural sources of selfless…

Motivated by a question of L. Robert, asking whether $\rm L(T(A)) = Lsc_{C}(T(A))$ for any separable C*-algebra A, we introduce and initiate the study of \emph{tracially reflexive C*-algebras}. We first prove that commutative C*-algebras…

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…

We write arbitrary separable nuclear C*-algebras as limits of inductive systems of finite-dimensional C*-algebras with completely positive connecting maps. The characteristic feature of such CPC*-systems is that the maps become more and…

Let $\Gamma$ be a discrete group. A $C^*$-algebra $A$ is an exotic $C^*$-algebra (associated to $\Gamma$) if there exist proper surjective $C^*$-quotients $C^*(\Gamma)\to A\to C^*_r(\Gamma)$. In this paper, we show that a large class of…

In this article, we consider the notion of almost irredundant sets: A subset $\mathcal{X}$ of a C*-algebra $\mathcal{A}$ is called almost irredundant if and only if for every $a\in \mathcal{X}$, the element $a$ does not belong to the…

We characterize the big Ramsey degrees of free amalgamation classes in finite binary languages defined by finitely many forbidden irreducible substructures, thus refining the recent upper bounds given by Zucker. Using this characterization,…

We introduce a new class of operator algebras -- tracially complete C*-algebras -- as a vehicle for transferring ideas and results between C*-algebras and their tracial von Neumann algebra completions. We obtain structure and classification…

We consider problems associated with the computation of spectra of self-adjoint operators in terms of the eigenvalue distributions of their n x n sections. Under rather general circumstances, we show how these eigenvalues accumulate near…

The notion of Fr\'{e}chet locally $C^*$-algebra generalizes the notion of $C^*$-algebra. In this paper, we first present some definitions and basic facts about locally $C^*$-algebra, and then we introduce and study the notion of ideal and…

We prove that faithful traces on separable and nuclear C*-algebras in the UCT class are quasidiagonal. This has a number of consequences. Firstly, by results of many hands, the classification of unital, separable, simple and nuclear…