Related papers: C*-Algebra Distance Filters

In this paper, we introduce a class of non-unital tracial approximation ${\rm C^*}$-algebras. Consider the class of ${\rm C^*}$-algebras which are tracially $\mathcal{Z}$-absorbing (in the sense of Amint, Golestani, Jamali, Phillips's…

To an arbitrary directed graph we associate a row-finite directed graph whose C*-algebra contains the C*-algebra of the original graph as a full corner. This allows us to generalize results for C*-algebras of row-finite graphs to…

We provide some background on the category of classifiable $\mathrm{C}^*$-algebras, whose objects are infinite-dimensional, simple, separable, unital $\mathrm{C}^*$-algebras that have finite nuclear dimension and satisfy the universal…

We show that nuclear C*-algebras have a refined version of the completely positive approximation property, in which the maps that approximately factorize through finite dimensional algebras are convex combinations of order zero maps. We use…

A classification is given of certain separable nuclear C*-algebras not necessarily of real rank zero, namely, the class of separable simple C*-algebras which are inductive limits of continuous-trace C*-algebras whose building blocks have…

We begin the systematic model theoretic study of $\mathrm{C}^*$-algebras using the tools of continuous logic.

We propose a new framework that generalizes the parameters of neural network models to $C^*$-algebra-valued ones. $C^*$-algebra is a generalization of the space of complex numbers. A typical example is the space of continuous functions on a…

We study semiprojective, subhomogeneous C*-algebras and give a detailed description of their structure. In particular, we find two characterizations of semiprojectivity for subhomogeneous C*-algebras: one in terms of their primitive ideal…

We generalize some aspects of the theory of compact projections relative to a C*-algebra, to the setting of more general algebras. Our main result is that compact projections are the decreasing limits of `peak projections', and in the…

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…

We study some general properties of tracial C*-algebras. In the first part, we consider Dixmier type approximation theorem and characterize symmetric amenability for C*-algebras. In the second part, we consider continuous bundles of tracial…

This is a survey of four recent papers which deal with the relationship of simple C*-algebras to the problem of computing the spectra of self-adjoint operators in the general case, especially when the spectrum is not discrete. It is an…

In this paper we analyze the structure of C*-algebras associated to ultragraphs, which are generalizations of directed graphs. We characterize the simple ultragraph algebras as well as deduce necessary and sufficient conditions for an…

An example is given of a simple, unital C*-algebra which contains an infinite and a non-zero finite projection. This C*-algebra is also an example of an infinite simple C*-algebra which is not purely infinite. A corner of this C*-algebra is…

In the paper we describe the C*-algebras of noncommutative spherical tight frames over some C*-algebras and then apply to study the noncommutative version of the universal classifying space.

Both boundary maps in K-theory are expressed in terms of surjections from projective C*-algebras to semiprojective C*-algebras.

Let $G=K\ltimes A$ be the semi-direct product group of a compact group $K$ acting on an abelian locally compact group $A$. We describe the $C^*$-algebra $C^*(G)$ of $G$ in terms of an algebra of operator fields defined over the spectrum of…

In this note we extend the construction of a $C^*$-algebra associated to a self-similar graph to the case of arbitrary countable graphs. We reduce the problem to the row-finite case with no sources, by using a desingularization process.…

Suppose $A$ is a separable unital $C(X)$-algebra each fibre of which is isomorphic to the same strongly self-absorbing and $K_{1}$-injective $C^{*}$-algebra $D$. We show that $A$ and $C(X) \otimes D$ are isomorphic as $C(X)$-algebras…

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…