Let A be a unital simple separable C∗-algebra with strict comparison of positive elements. We prove that the Cuntz semigroup of A is recovered functorially from the Murray–von Neumann semigroup and the tracial state space T(A) whenever the extreme boundary of T(A) is compact and of finite covering dimension. Combined with a result of Winter, we obtain Z ⊗ A ∼= A whenever A moreover has locally ...

Let B be a σ–unital C–algebra. We show that every strongly continuous E0–semigroup on the algebra of adjointable operators on a full Hilbert B–module E gives rise to a full continuous product system of correspondences over B. We show that every full continuous product system of correspondences over B arises in that way. If the product system is countably generated, then E can be chosen countabl...

For a locally compact group G, the measure convolution algebra M(G) carries a natural coproduct. In previous work, we showed that the canonical predual C0(G) of M(G) is the unique predual which makes both the product and the coproduct on M(G) weak∗-continuous. Given a discrete semigroup S, the convolution algebra l(S) also carries a coproduct. In this paper we examine preduals for l(S) making b...

Let A be a simple, unital, finite, and exact C-algebra which absorbs the Jiang-Su algebra Z tensorially. We prove that the Cuntz semigroup of A admits a complete order embedding into an ordered semigroup which is obtained from the Elliott invariant in a functorial manner. We conjecture that this embedding is an isomorphism, and prove the conjecture in several cases. In these same cases — Z-stab...

It is proved that the unital Banach algebra of almost periodic functions of several variables with Bohr-Fourier spectrum in a given additive semigroup is an Hermite ring. The same property holds for the Wiener algebra of functions that in addition have absolutely convergent Bohr-Fourier series. As applications of the Hermite property of these algebras, we study factorizations of Wiener–Hopf typ...

Certain criteria are demonstrated for a spatial derivation of a von Neumann algebra to generate a one-parameter semigroup of endomorphisms of that algebra. These are then used to establish a converse to recent results of Borchers and of Wiesbrock on certain one-parameter semigroups of endomorphisms of von Neumann algebras (specifically, Type III1 factors) that appear as lightlike translations i...

The structure of the endomorphism monoid of a stable basis algebra A is described. It is shown to be an abundant monoid; the subsemigroup of endomorphisms of finite rank has a regular semigroup of left quotients. This is a revised version of the article that appeared in Algebra Universalis 51 (2004), 257− −285. The authors are grateful to Professor George Bergman for correcting their original d...

We introduce a new class of noncommutative rings-Galois orders, realized as certain subrings of invariants in skew semigroup rings, and develop their structure theory. The class of Galois orders generalizes classical orders in noncommutative rings and contains many classical objects, such as the Generalized Weyl algebras, the universal enveloping algebra of the general linear Lie algebra, assoc...