The invertible elements are dense in the irrational rotation C*-algebras.
The Kolmogorov Entropy For Quantum Systems Revisited.
The Linear Groups of Injective Factors and of Matroid C*Algebras are Contractible to a Point.
The Local Index Formula in Noncommutative Geometry.
The partial-isometric crossed products of by the forward and backward shifts.
The Powers sum of spatial CPD-semigroups and CP-semigroups
We define spatial CPD-semigroups and construct their Powers sum. We construct the Powers sum for general spatial CP-semigroups. In both cases, we show that the product system of that Powers sum is the product of the spatial product systems of its factors. We show that on the domain of intersection, pointwise bounded CPD-semigroups on the one side and Schur CP-semigroups on the other, the constructions coincide. This summarizes all known results about Powers sums and generalizes them considerably....
The relative Dixmier property for inclusions of von Neumann algebras of finite index
The stabilisation trick for coactions.
The structure of higher-dimensional noncommutative tori and metric diophantine approximation.
The unitary implementation of a measured quantum groupoid action
Mimicking the von Neumann version of Kustermans and Vaes’ locally compact quantum groups, Franck Lesieur had introduced a notion of measured quantum groupoid, in the setting of von Neumann algebras. In a former article, the author had introduced the notions of actions, crossed-product, dual actions of a measured quantum groupoid; a biduality theorem for actions has been proved. This article continues that program: we prove the existence of a standard implementation for an action, and a biduality...
Topological orbit equivalence and C*-crossed products.
Towards a Galois theory for crossed products of C*-algebras.
Tracial states on crossed products associated with Furstenberg transformations on the 2-torus
Trivial fixed point subalgebras of the rotation algebra.
Trivial noncommutative principal torus bundles
A (smooth) dynamical system with transformation group ⁿ is a triple (A,ⁿ,α), consisting of a unital locally convex algebra A, the n-torus ⁿ and a group homomorphism α: ⁿ → Aut(A), which induces a (smooth) continuous action of ⁿ on A. In this paper we present a new, geometrically oriented approach to the noncommutative geometry of trivial principal ⁿ-bundles based on such dynamical systems, i.e., we call a dynamical system (A,ⁿ,α) a trivial noncommutative principal ⁿ-bundle if each isotypic component...
Twisted crossed products of C*-algebras. II.
Twisted group C*-algebras corresponding to nilpotent discrete groups.
Unique state extension and hereditary C*-subalgebras.
Unitaires multiplicatifs et dualité pour les produits croisés de -algèbres
Universally weakly inner one-parameter automorphism groups of seperable C*-algebras, II.