Related papers: The Corona Factorization Property and Refinement M…

An algebra is said to be quasi-directly finite when any left-invertible element in its unitization is automatically right-invertible. It is an old observation of Kaplansky that the von Neumann algebra of a discrete group has this property;…

We introduce the Property (C) for a unital commutative sub-C*-algebra $D$ of a unital C*-algebra $A$, a version of the relative comparison property using almost normalizers. Under the assumption of this property, the $\mathcal Z$-absorption…

Let $A$ be a stably finite simple unital $C^*$-algebra and suppose $\alpha $ is an action of a finite group $G$ with the tracial Rokhlin property. Suppose further $A$ has real rank zero and the order on projections over $A$ is determined by…

We study projections in the corona algebra of $C(X)\otimes K$ where $X=[0,1],[0,\infty),(-\infty,\infty)$, and $[0,1]/\{0,1 \}$. Using BDF's essential codimension, we determine conditions for a projection in the corona algebra to be…

In this paper we introduce an analog of the tracial Rokhlin property, called the {\emph {projection free tracial Rokhlin property}}, for $C^*$-algebras which may not have any nontrivial projections. Using this we show that if $A$ is an…

We generalize the classification result of Restorff on Cuntz-Krieger algebras to cover all unital graph C*-algebras with real rank zero, showing that Morita equivalence in this case is determined by ordered, filtered K-theory as conjectured…

Let $M$ be a cancellative commutative monoid and call a submonoid $S$ of $M$ an undermonoid if $\G(S)=\G(M)$ inside the Grothendieck group of $M$. Gotti and Li asked whether the finite factorization property is hereditary once it is known…

Let $G$ be a finite group, let $A$ be an infinite-dimensional stably finite simple unital C*-algebra, and let $\alpha \colon G \to \operatorname{Aut} (A)$ be a tracially strictly approximately inner action of $G$ on $A$. Then the radius of…

We study a tracial notion of Z-absorption for simple, unital C*-algebras. We show that if A is a C*-algebra for which this property holds then A has almost unperforated Cuntz semigroup, and if in addition A is nuclear and separable we show…

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…

In his study of the relative Dixmier property for inclusions of von Neumann algebras and of $C^*$-algebras, Popa considered a certain property of automorphisms on $C^*$-algebras, that we here call the strong averaging property. In this note…

This paper introduces a canonical Polish groupoid associated to any separable unital C*-algebra, termed the unitary conjugation groupoid. It is defined as the semidirect product of the algebra's dual space by its unitary group, acting by…

We characterize the class of RFD $C^*$-algebras as those containing a dense subset of elements that attain their norm under a finite-dimensional representation. We show further that this subset is the whole space precisely when every…

We prove implications among the conditions in the title for an inclusion of a C*-algebra A in a C*-algebra B, and we also relate this to several other properties in case B is a crossed product for an action of a group, inverse semigroup or…

Let $\Fth$ be a single vertex \textsf{k}-graph, and $\pi_\omega(\O_\theta)"$ be the von Neumann algebra induced from the GNS representation of a distinguished state $\omega$ of its $\textsf{k}$-graph C*-algebra $\O_\theta$. In this paper,…

We show that the following properties of unital ${\rm C^*}$-algebra in a class of $\Omega$ are preserved by unital simple ${\rm C^*}$-algebra in the class of $\rm WTA\Omega$: $(1)$ uniform property $\Gamma$, $(2)$ a certain type of tracial…

We introduce and study a notion of Rokhlin property for an inclusion of unital $C^*$-algebras which could have no projections like the Jiang-Su algebra. We also introduce a notion of approximate representability and show a duality between…

Let E be a row-finite directed graph. We prove that there exists a C*-algebra C*_{min}(E) with the following co-universal property: given any C*-algebra B generated by a Toeplitz-Cuntz-Krieger E-family in which all the vertex projections…

Given a closed ideal $I$ in a C*-algebra $A$, we show that $A$ is pure if and only if $I$ and $A/I$ are pure. More generally, we study permanence of comparison and divisibility properties when passing to extensions. As an application we…

We prove a number of fundamental facts about the canonical order on projections in C*-algebras of real rank zero. Specifically, we show that this order is separative and that arbitrary countable collections have equivalent (in terms of…