Related papers: Open Projections and Suprema in the Cuntz Semigrou…
We generalize some technical results of Glicksberg to the realm of general operator algebras and use them to give a characterization of open and closed projections in terms of certain multiplier algebras. This generalizes a theorem of J.…
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 answer a question of Takesaki by showing that the following can be derived from the thesis of N-T Shen: If A and B are sigma-unital hereditary C*-subalgebras of C such that ||p - q|| < 1, where p and q are the corresponding open…
We prove a number of fundamental facts about the canonical order on projections in C*-algebras of real rank zero. Specifically, we show that this order is separative and that arbitrary countable collections have equivalent (in terms of…
It is shown that the Cuntz semigroup of a space with dimension at most two, and with second cohomology of its compact subsets equal to zero, is isomorphic to the ordered semigroup of lower semicontinuous functions on the space with values…
To an $r$-dimensional subshift of finite type satisfying certain special properties we associate a $C^*$-algebra $\cA$. This algebra is a higher rank version of a Cuntz-Krieger algebra. In particular, it is simple, purely infinite and…
The (abstract) Cuntz algebra is generated by non-unitary isometries and has therefore no intrinsic finiteness properties. To approximate the elements of the Cuntz algebra by finite-dimensional objects, we thus consider a spatial…
It is shown that the Cuntz semigroup is a complete invariant for the C*-algebras that can be realized as an inductive limit of a sequence of finite direct sums of splitting interval algebras.
We study semiprojective, subhomogeneous C*-algebras and give a detailed description of their structure. In particular, we find two characterizations of semiprojectivity for subhomogeneous C*-algebras: one in terms of their primitive ideal…
The class of separable C*-algebras which can be written as inductive limits of continuous-trace C*-algebras with spectrum homeomorphic to a disjoint union of trees and trees with a point removed is classified by the Cuntz semigroup.
In this paper, we introduce the concept of trace-open projections in the second dual A** of a C*-algebra A, and we show that if there is a faithful normal semi-finite trace T on A**, and 1 is a T-open projection, then each 2-local…
We introduce the notion of the partial group algebra with projections and relations and show that this C*-algebra is a partial crossed product. Examples of partial group algebras with projections and relations are the Cuntz-Krieger algebras…
In this article we survey some of the recent goings-on in the classification programme of C$^*$-algebras, following the interesting link found between the Cuntz semigroup and the classical Elliott invariant and the fact that the Elliott…
We study the Cuntz semigroup for non-simple $\text{C}^*$-algebras in this paper. In particular, we use the extended Elliott invariant to characterize the Cuntz comparison for $\text{C}^*$-algebras with the projection property which have…
We study comparison properties in the category Cu aiming to lift results to the C*-algebraic setting. We introduce a new comparison property and relate it to both the CFP and $\omega$-comparison. We show differences of all properties by…
Let X be a product system over a quasi-lattice ordered group. Under mild hypotheses, we associate to X a C*-algebra which is co-universal for injective Nica covariant Toeplitz representations of X which preserve the gauge coaction. Under…
We revisit a well-known "surjectivity onto quotient" type lemma of Kirchberg on the central sequence algebra of a separable unital ${\rm C}^*$-algebra, and use it to prove a "surjectivity onto quotient" result on approximately inner…
The study of open quantum systems relies on the notion of unital completely positive semigroups on $C^*$-algebras representing physical systems. The natural generalisation would be to consider the unital completely positive semigroups on…
We say that a C*-algebra is nowhere scattered if none of its quotients contains a minimal open projection. We characterize this property in various ways, by topological properties of the spectrum, by divisibility properties in the Cuntz…
The note is concerned with inductive systems of Toeplitz algebras and their $*$-homomorphisms over arbitrary partially ordered sets. The Toeplitz algebra is the reduced semigroup $C^*$-algebra for the additive semigroup of non-negative…