Related papers: The isomorphism relation for separable C*-algebras

We give sufficient conditions allowing one to build a C*-algebraic structure on a self-adjoint linear subspace of a C*-algebra in such a way that the subspace is naturally identified with the resulting C*-algebra via a completely positive…

We show that every groupoid C*-algebra is isomorphic to its opposite, and deduce that there exist C*-algebras that are not stably isomorphic to groupoid C*-algebras, though many of them are stably isomorphic to twisted groupoid C*-algebras.…

We study the class of Borel equivalence relations under continuous reducibility. In particular , we characterize when a Borel equivalence relation with countable equivalence classes is $\Sigma$ 0 $\xi$ (or $\Pi$ 0 $\xi$). We characterize…

Every separable nondegenerate C*-correspondence over a commutative C*-algebra with discrete spectrum is isomorphic to a graph correspondence.

Generalizing the notion of a multiplicative unitary (in the sense of Baaj-Skandalis), which plays a fundamental role in the theory of locally compact quantum groups, we develop in this paper the notion of a multiplicative partial isometry.…

We show that if A is a separable, nuclear, O_infty-absorbing (or strongly purely infinite) C*-algebra, which is homotopic to zero in an ideal-system preserving way, then A is the inductive limit of C*-algebras of the form M_k(C_0(G,v)),…

We show that the class of all Banach spaces which are isomorphic to $ c_{0} $ is a complete analytic set with respect to the Effros Borel structure of separable Banach spaces. The proof employs a recent Bourgain-Delbaen construction by…

A class of $C^*$-algebras, to be called those of generalized tracial rank one, is introduced, and classified by the Elliott invariant. A second class of unital simple separable amenable $C^*$-algebras, those whose tensor products with…

We study the complexity of the space $C^*_p(X)$ of bounded continuous functions with the topology of pointwise convergence. We are allowed to use descriptive set theoretical methods, since for a separable metrizable space $X$, the…

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…

Gao and Jackson showed that any countable Borel equivalence relation (CBER) induced by a countable abelian Polish group is hyperfinite. This prompted Hjorth to ask if this is in fact true for all CBERs classifiable by (uncountable) abelian…

We prove that uniformly locally finite metric spaces with isomorphic Roe algebras must be coarsely equivalent. As an application, we also prove that the outer automorphism group of the Roe algebra of a metric space of bounded geometry is…

We consider inductive systems of C*-algebras with completely positive contractive connecting maps. We define a condition, called C*-encoding, which is sufficient for the limit of the system to be completely order isomorphic to a C*-algebra…

We study the existence of minimal dynamical systems, their orbit and minimal orbit-breaking equivalence relations, and their applications to C*-algebras and K-theory. We show that given any finite CW-complex there exists a space with the…

We show that the class of unital $\mathrm{C}^*$-algebras is an elementary class in the language of operator systems. As a result, we have that there is a definable predicate in the language of operator systems that defines the…

In this work we construct a C*-algebra from an injective endomorphisms of some group G, allowing the endomorphism to have infinite cokernel. We generalize results obtained by I. Hirshberg and also by J. Cuntz and A. Vershik. In good cases…

For any unital separable simple infinite-dimensional nuclear C*-algebra with finitely many extremal traces, we prove that Z-absorption, strict comparison, and property (SI) are equivalent. We also show that any unital separable simple…

In this paper we show that the $\mathrm{K}$-homology groups of a separable C*-algebra can be enriched with additional descriptive set-theoretic information, and regarded as definable groups. Using a definable version of the Universal…

We define E-theory for separable C*-algebras over second countable topological spaces and establish its basic properties. This includes an approximation theorem that relates the E-theory over a general space to the E-theories over finite…

We show that the homology of the partition algebras, interpreted as appropriate Tor-groups, is isomorphic to that of the symmetric groups in a range of degrees that increases with the number of nodes. Furthermore, we show that when the…