Related papers: Korovkin-type properties for completely positive m…

We say that a contractive Hilbert space operator is universal if there is a natural surjection from its generated C*-algebra to the C*-algebra generated by any other contraction. A universal contraction may be irreducible or a direct sum of…

We consider positive semidefinite kernels valued in the $*$-algebra of continuous and continuously adjointable operators on a VH-space (Vector Hilbert space in the sense of Loynes) and that are invariant under actions of $*$-semigroups. For…

We prove a uniqueness theorem and give a characterization of simplicity for Steinberg algebras associated to non-Hausdorff ample groupoids. We also prove a uniqueness theorem and give a characterization of simplicity for the C*-algebra…

The Kasparov absorption (or stabilization) theorem states that any countably generated Hilbert C*-module is isomorphic to a direct summand in the standard module of square summable sequences in the base C*-algebra. In this paper, this…

We prove that a number of classes of separable unital C*-algebras are closed under crossed products by finite group actions with the Rokhlin property, including: (1) AI algebras, AT algebras, and related classes characterized by direct…

We show that a $KK$-equivalence between two unital $C^*$-algebras produces a correspondence between their DG categories of finitely generated projective modules which is a $\mathbf{K}_*$-equivalence, where $\mathbf{K}_*$ is Waldhausen's…

Conventional discrete approximations of a manifold do not preserve its nontrivial topological features. In this article we describe an approximation scheme due to Sorkin which reproduces physically important aspects of manifold topology…

The construction of a C*-algebra of a differential groupoid is presented. It is shown that it defines a covariant functor from the category of differential groupoids in a sense of S. Zakrzewski to the category of C*-algebras.

We show that semigroup C*-algebras attached to ax+b-semigroups over rings of integers determine number fields up to arithmetic equivalence, under the assumption that the number fields have the same number of roots of unity. For finite…

We introduce the spatial Rokhlin property for actions of coexact compact quantum groups on $\mathrm{C}^*$-algebras, generalizing the Rokhlin property for both actions of classical compact groups and finite quantum groups. Two key…

Let A be a unital separable C*-algebra, and D a K_1-injective strongly self-absorbing C*-algebra. We show that if A is D-absorbing, then the crossed product of A by a compact second countable group or by Z or by R is D-absorbing as well,…

In this memoir we develop a framework to study rigidity problems for Roe-like C*-algebras of countably generated coarse spaces. The main goal is to give a complete and self-contained solution to the problem of C*-rigidity for proper…

We construct commutative algebra spectra that represent the operator $K$-theory of $C^*$-algebras, which are algebras over the commutative ring spectra that represent topological $K$-theory. The spectral multiplicative structure introduces…

Let $G$ be a locally compact group with cocompact connected component. We prove that the assembly map from the topological $\k$-theory of $G$ to the $\k$-theory of the reduced $C^*$-algebra of $G$ is an isomorphism.

We prove that every bounded, positive, irreducible, stochastically continuous semigroup on the space of bounded, measurable functions which is strong Feller, consists of kernel operators and possesses an invariant measure converges…

We prove stability theorems in the Cuntz semigroup of a commutative C*-algebra which are analogues of classical stability theorems for topological vector bundles over compact Hausdorff spaces. Several applications to simple unital AH…

In this paper, we first study the local rings of a Berkovich analytic space from the point of view of commutative algebra. We show that those rings are excellent ; we introduce the notion of a an analytically separable extension of…

In this article, we consider algebras $\mathcal{A}$ of non-formal pseudodifferential operators over $S^1$ which contain $C^\infty(S^1),$ understood as multiplication operators. We apply a construction of Chern-Weil type forms in order to…

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…

Approximation theory has long been concerned with the development of positive linear operators that effectively approximate classes of functions. Among the most well-known results in this area are Korovkin-type approximation theorems, which…