Related papers: A Mayer-Vietoris Spectral Sequence for C*-Algebras…

Exploiting the graph product structure and results concerning amalgamated free products of C*-algebras we provide an explicit computation of the K-theoretic invariants of right-angled Hecke C*-algebras, including concrete algebraic…

We study multivariate generalisations of the classical Wiener--Hopf algebra, which is the C$^*$-algebra generated by the Wiener--Hopf operators, given by the convolutions restricted to convex cones. By the work of Muhly and Renault, this…

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…

We use C*-algebra theory to provide a new method of decomposing the eseential spectra of self-adjoint and non-self-adjoint Schrodinger operators in one or more space dimensions.

We analyze the sequence obtained by consecutive applications of the Cantor-Bendixson derivative for a noncommutative scattered $C^*$-algebra $\mathcal A$, using the ideal $\mathcal I^{At}(\mathcal A)$ generated by the minimal projections of…

K-theory and Ext are computed for the C*-algebra C*(E) of any countable directed graph E. The results generalize the K-theory computations of Raeburn and Szymanski and the Ext computations of Tomforde for row-finite graphs. As a…

Given a graph of C*-algebras, we prove a long exact sequence in KK-theory for both the maximal and the vertex-reduced fundamental C*-algebras in the presence of possibly non GNS-faithful conditional expectations. We deduce from it the…

Let $\sigma$ be the involution of the Roe algebra $\Roe{\RR}$ which is induced from the reflection $\RR\to\RR; x\mapsto -x$. A graded Fredholm module over a separable $C^*$-algebra $A$ gives rise to a homomorphism…

We compute the K-theory of a collection of C*-algebras, which we refer to as boundary C*-algebras, arising as the crossed product C*-algebras of lattice actions on the maximal Furstenberg boundaries of symmetric spaces of noncompact type.…

In this paper, we apply quantitative operator K-theory to develop an algorithm for computing K-theory for the class of filtered C *-algebras with asymptotic finite nuclear decomposition. As a consequence, we prove the K{\"u}nneth formula…

Let $X$ be a metric measure space. A Delone subset $D\subset X$ is a uniformly discrete set coarsely equivalent to $X$. We consider the space $\mathcal D_F$ of controlled Delone subsets of $X$ with an appropriate metric, and show that it,…

We give a classification result for a certain class of $C^{*}$-algebras $\mathfrak{A}$ over a finite topological space $X$ in which there exists an open set $U$ of $X$ such that $U$ separates the finite and infinite subquotients of…

We introduce the concept of finitely coloured equivalence for unital *-homomorphisms between C*-algebras, for which unitary equivalence is the 1-coloured case. We use this notion to classify *-homomorphisms from separable, unital, nuclear…

By the Gelfand-Naimark theorem, any C*-algebra is isometrically isomorphic to a *-algebra of bounded operators on a Hilbert space which is closed with respect to the topology induced by the operator norm. Hence, the C*-algebras furnish an…

We show that the following conditions on a C*-algebra are equivalent: (i) it has the fixed point property for nonexpansive mappings, (ii) the spectrum of every self adjoint element is finite, (iii) it is finite dimensional. We prove that…

For a positive element $A$ of a $C^*$-algebra $\mathfrak{A}$, let ${\|X\|}_{A}$ denote the $A$-operator semi-norm of $X\in\mathfrak{A}$. In this paper, we aim to introduce and study the notion of $A$-spectrum for $X$ such that…

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 formulate a Mayer--Vietoris/\v{C}ech viewpoint on $K$-theory for crossed products by discrete quantum groups, emphasizing how local-to-global gluing data interacts with quantum-group coefficients. Starting from a $G$-equivariant ideal…

We define continuous C*-algebras over a topological space X and establish some basic results. If X is a locally compact Hausdorff space, continuous C*-algebras over X are equivalent to ordinary continuous C_0(X)-algebras. The main purpose…

A C*-algebra is determined to a great extent by the partial order of its commutative C*-algebras. We study order-theoretic properties of this dcpo. Many properties coincide: the dcpo is, equivalently, algebraic, continuous, meet-continuous,…