Related papers: Trace Asymptotics for C*-Algebras from Smale Space…
In this paper we survey our recent work on C*-correspondences and their associated operator algebras; in particular, on adding tails, the Shift Equivalence Problem and Hilbert bimodules.
We study the uniform property $\Gamma$ for separable simple $C^*$-algebras which have quasitraces and may not be exact. We show that a stably finite separable simple $C^*$-algebra $A$ with strict comparison and uniform property $\Gamma$ has…
We investigate conditions on a graph $C^*$-algebra for the existence of a faithful semifinite trace. Using such a trace and the natural gauge action of the circle on the graph algebra, we construct a smooth $(1,\infty)$-summable semfinite…
We consider AF-flows, i.e., one-parameter automorphism groups of a unital simple C*-algebra which leave invariant the dense union of an increasing sequence of finite-dimensional *-subalgebras, and derive two properties for these; an absence…
We show that semiprojectivity of a C*-algebra is preserved when passing to C*-subalgebras of finite codimension. In particular, any pullback of two semiprojective C*-algebras over a finite-dimensional C*-algebra is again semiprojective.
Universal continuous calculi are defined and it is shown that for every finite tuple of pairwise commuting Hermitian elements of a Su*-algebra (an ordered *-algebra that is symmetric, i.e. "strictly" positive elements are invertible, and…
We study the simplicity of $C^{*}$-algebras built from group actions. For a faithful isometric action of a group $G$ on a countable metric space $X$, we use the associated action representation on $\ell^2(X)$ to define the action-based…
An AF C*-algebra has a natural filtration as an increasing sequence of finite dimensional C*-algebras. We show that it is possible to construct a Dirac operator which relates to this filtration in a natural way and which will induce a…
We will investigate the intersection of the normal operators with the closure of the nilpotent and quasinilpotent operators in various C*-algebras. A complete characterization will be given for type I and type III von Neumann algebras with…
We conjecture that a unital C$^*$-algebra is a W$^*$-algebra if and only if each of its maximal abelian self-adjoint subalgebras is a W$^*$-algebra; this is a space-free analogue of a known result due to G.K. Pedersen. Our main result is a…
This paper studies the problems of embedding and isomorphism for countably generated Hilbert C*-modules over commutative C*-algebras. When the fibre dimensions differ sufficiently, relative to the dimension of the spectrum, we show that…
We extend in this paper several results of E. Kirchberg, S. Wassermann and the author dealing with continuous fields of C*--algebras to the semi-continuous case. We provide a new characterisation of separable lower semi-continuity…
A precise description of the injective envelope of a spatial continuous trace C*-algebra A over a Stonean space Delta is given. The description is based on the notion of a weakly continuous Hilbert bundle, which we show to be a…
We describe a special class of representations of an inverse semigroup S on Hilbert's space which we term "tight". These representations are supported on a subset of the spectrum of the idempotent semilattice of S, called the "tight…
We consider an action of the circle group, T on a von Neumann algebra, M. Similarly to the case when the algebra of essentially bounded functions on T is acted upon by translations, we define the generalized Hardy subspace of H,where H is…
For a locally compact group $G$ we look at the group algebras $C_0(G)$ and $C_r^*(G)$, and we let $f\in C_0(G)$ act on $L^2(G)$ by the multiplication operator $M(f)$. We show among other things that the following properties are equivalent:…
Given two C*-algebras A and B, abstract A-B bimodules that can be isometrically represented as operator bimodules are characterised in terms of their norm. Various properties of such bimodules are given. Their theory is very similar to…
Kadison and Kastler introduced a metric on the set of all C$^*$-algebras on a fixed Hilbert space. In this paper structural properties of C$^*$-algebras which are close in this metric are examined. Our main result is that the property of…
The C*-envelope of the limit algebra (or limit space) of a contractive regular system of digraph algebras (or digraph spaces) is shown to be an approximately finite C*-algebra and the direct system for the C*-envelope is determined…
We geometrically describe the relation induced on a set of graphs by isomorphism of their associated graph C*-algebras as the smallest equivalence relation generated by five types of moves. The graphs studied have finitely many vertices and…