Related papers: Quantifier elimination in C*-algebras

We show that it is consistent with ZFC that there is a simple nuclear non-separable C*-algebra which is not isomorphic to its opposite algebra. We can furthermore guarantee that this example is an inductive limit of unital copies of the…

We describe a class of $C^*$-algebras which simultaneously generalise the ultragraph algebras of Tomforde and the shift space $C^*$-algebras of Matsumoto. In doing so we shed some new light on the different $C^*$-algebras that may be…

We discuss the existence of (injectively) universal C*-algebras and prove that all C*-algebras of density character $\aleph_1$ embed into the Calkin algebra, $Q(H)$. Together with other results, this shows that each of the following…

It has been a longstanding problem whether every amenable operator algebra is isomorphic to a (necessarily nuclear) C*-algebra. In this note, we give a nonseparable counterexample. The existence of a separable counterexample remains an open…

Examples of simple, separable, unital, purely infinite $C^*$--algebras are constructed, including: (1) some that are not approximately divisible; (2) those that arise as crossed products of any of a certain class of $C^*$--algebras by any…

Connectivity is a homotopy invariant property of separable C*-algebras which has three notable consequences: absence of nontrivial projections, quasidiagonality and a more geometric realization of KK-theory for nuclear C*-algebras using…

A countable group is C*-simple if its reduced C*-algebra is a simple algebra. Since Powers recognised in 1975 that non-abelian free groups are C*-simple, large classes of groups which appear naturally in geometry have been identified,…

We give a classification theorem for a class of C*-algebras which are direct limits of extensions of circle algebras by purely infinite C*-algebras. The invariant consists of the following: (1) the set of Murray-von Neumann equivalence…

Let $K$ be a compact metric space and let $\gamma = (\gamma_1, \dots, \gamma_n)$ be a system of proper contractions on $K$. We study a C*-algebra $\mathcal{MC}_{\gamma_1, \dots, \gamma_n}$ generated by all multiplication operators by…

We consider various quotients of the C*-algebra of bounded operators on a nonseparable Hilbert space, and prove in some cases that, consistently, there are many outer automorphisms.

We study nonunital $C^*$-algebras such that for any element there exists a local unit and prove that in such algebras there are no frames. This fact was previously known only for commutative algebras. Among other results, we establish some…

It is well known that "bad" quotient spaces (typically: non-Hausdorff) can be studied by associating to them the groupoid C*-algebra of an equivalence relation, that in the "nice" cases is Morita equivalent to the C*-algebra of continuous…

In this paper we introduce the M\"obius disjointness for C$^*$-algebras with their automorphisms and studied the M\"obius disjointness for finite dimensional C$^*$ algebras, finite von Neumann algebras, reduced free group algebra and…

For a completely Hausdorff quasi-topological group $G$, we construct a universal pro-$C^*$-algebra $C(E^+G)$ as the non-commutative geometer's analogue of the total space $EG$ of the classifying principal $G$-bundle $EG\to BG$. The…

We prove quantifier elimination for the theory of quasi-real closed fields with a compatible valuation. This unifies the same known results for algebraically closed valued fields and real closed valued fields.

We define the notion of quantized function algebras at $q=0$ or crystallization of the $q$ deformations of the type $A_{n}$ compact Lie groups at the $C^*$-algebra level. The $C^{*}$-algebra $A_{n}(0)$ is defined as a universal…

Given an arbitrary countable ordinal $\alpha $, we introduce the notion of type $I_{\alpha }$ C*-algebra and $\alpha $-subhomogeneous C*-algebra. When $\alpha =0$, these recover the notions of Fell C*-algebra and of commutative C*-algebra,…

The goal of this paper is twofold. In addition to the results stated in the next paragraph, we present some classical results on absoluteness relevant to functional analysis that are well known to logicians but not nearly as well advertised…

We classify all essential extensions of the form $$0 \rightarrow \W \rightarrow \D \rightarrow A \rightarrow 0$$ where $\W$ is the unique separable simple C*-algebra with a unique tracial state, with finite nuclear dimension and with…

We prove that the zeroth L^2-Betti number of a compact quantum group vanishes unless the underlying C*-algebra is finite dimensional and that the zeroth L^2-homology itself is non-trivial exactly when the quantum group is coamenable.