Related papers: Some properties for certain generalized tracial ap…

We show that the Fra\"iss\'e limit of a category of unital separable $C^*$-algebras which is sufficiently closed under tensor products of its objects and morphisms is strongly self-absorbing, given that it has approximate inner half-flip.…

This article continues the investigation of the tracial geometry of classifiable $\mathrm{C}^*$-algebras that have real rank zero and stable rank one. Using the language of optimal transport, we describe several situations in which the…

Using various finite dimensional approximation properties, four convex subsets of the tracial space of a unital C*-algebra are defined. Applications of these tracial invariants include: (1) An analogue of Szego's limit theorem for arbitrary…

We study the problem of extending a state on an abelian $C^*$- subalgebra to a tracial state on the ambient $C^*$-algebra. We propose an approach that is well-suited to the case of regular inclusions, in which there is a large supply of…

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 give an example of an exact, stably finite, simple. separable C*-algebra D which is not isomorphic to its opposite algebra. Moreover, D has the following additional properties. It is stably finite, approximately divisible, has real rank…

Nuclear $C^*$-algebras having a system of completely positive approximations formed with convex combinations of a uniformly bounded number of order zero summands are shown to be approximately finite dimensional.

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…

It is shown that projectionless C*-algebras that tensorially absorb the Jiang-Su algebra have the property that every element is a limit of products of two nilpotents. This is then used to classify the approximate unitary equivalence…

We exhibit examples of simple separable nuclear C*-algebras, along with actions of the circle group and outer actions of the integers, which are not equivariantly isomorphic to their opposite algebras. In fact, the fixed point subalgebras…

An algebra $\mathcal{A}$ of $n\times n$ complex matrices is said to be \textit{idempotent compressible} if $E\mathcal{A}E$ is an algebra for all idempotents $E\in\mathbb{M}_n(\mathbb{C})$. Analogously, $\mathcal{A}$ is said to be…

We develop the concept of weak tracial Rokhlin property for finite group actions on simple (not necessarily unital) C*-algebras and study its properties systematically. In particular, we show that this property is stable under restriction…

Let $C$ and $A$ be two unital separable amenable simple C*-algebras with tracial rank no more than one. Suppose that $C$ satisfies the Universal Coefficient Theorem and suppose that $\phi_1, \phi_2: C\to A$ are two unital monomorphisms. We…

We show that a separable C*-algebra is an inductive limits of projective C*-algebras if and only if it has trivial shape, that is, if it is shape equivalent to the zero C*-algebra. In particular, every contractible C*-algebra is an…

We exhibit examples of actions of countable discrete groups on both simple and non-simple nuclear stably finite C*-algebras that are tracially amenable but not amenable. We furthermore obtain that, under the additional assumption of strict…

We initiate the study of compact group actions on C*-algebras from the perspective of model theory, and present several applications to C*-dynamics. Firstly, we prove that the continuous part of the central sequence algebra of a strongly…

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…

Let $n$ be a natural number. Recall that a C*-algebra is said to be $n$-subhomogeneous if all its irreducible representations have dimension at most $n$. In this short note, we give various approximation properties characterising…

Let $A$ be an infinite-dimensional unital simple C*-algebra such that A has $\mu$-$oz{\rm LLP}$ property for any $\mu\in(0,1)$. Let $B\subseteq A$ be a centrally large subalgebra of $A$ such that $B$ has tracial topological rank zero. Then…

We introduce and characterize a particularly tractable class of unital type 1 C*-algebras with bounded dimension of irreducible representations. Algebras in this class are called recursive subhomogeneous algebras, and they have an inductive…