Takesaki's duality for a non-degenerate co-action.
The action of groups on real factors of type III, .
The adic realizations of the ergodic actions with the homeomorphisms of the Markov compact and the ordered Bratteli diagrams
The C*-algebras of codimension one foliations without holonomy.
The cyclic homology of crossed product algebras.
The cyclic homology of crossed product algebras, II. Topological algebras.
The graph traces of finite graphs and applications to tracial states of -algebras.
The intrinsic invariant of an approximately finite dimensional factor and the cocycle conjugacy of discrete amenable group actions.
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.