The -pseudodifferential calculus on Galois coverings and a higher Atiyah-Patodi-Singer index theorem
The Baum-Connes conjecture.
The Baum-Connes conjecture, noncommutative Poincaré duality, and the boundary of the free group.
The Bisognano-Wichmann theorem for charged states and the conformal boundary of a black hole.
The bundle convergence in von Neumann algebras and their -spaces
A stronger version of almost uniform convergence in von Neumann algebras is introduced. This "bundle convergence" is additive and the limit is unique. Some extensions of classical limit theorems are obtained.
The -algebra of a Hilbert bimodule
Un -modulo hilbertiano destro su una -algebra dotato di uno -omomorfismo isometrico viene qui considerato come un oggetto della -categoria degli -moduli Hilbertiani destri. Come in [11], associamo ad esso una -algebra contenente come un «-bimodulo hilbertiano in ». Se è pieno e proiettivo finito è la -algebra , la generalizzazione delle algebre di Cuntz-Krieger introdotta da Pimsner [27] (e in un caso particolare da Katayama [31]). Più in generale, è canonicamente immersa...
The -algebras of row-finite graphs.
The C*-algebra generated by two projections.
The C*-Algebra of a Singular Elliptic Problem on a Noncompact Riemannian Manifold.
The C*-algebras of codimension one foliations without holonomy.
The canonical endomorphism for infinite index inclusions.
The centralizer under tensor product.
The closed Friedman world model with the initial and final singularities as a non-commutative space
The most elegant definition of singularities in general relativity as b-boundary points, when applied to the closed Friedman world model, leads to the disastrous situation: both the initial and final singularities form the single point of the b-boundary which is not Hausdorff separated from the rest of space-time. We apply Alain Connes' method of non-commutative geometry, defined in terms of a C*-algebra, to this case. It turns out that both the initial and final singularities can be analysed as...
The closure of the invertibles in a von Neumann algebra
In this paper we consider a subset  of a Banach algebra A (containing all elements of A which have a generalized inverse) and characterize membership in the closure of the invertibles for the elements of Â. Thus our result yields a characterization of the closure of the invertible group for all those Banach algebras A which satisfy  = A. In particular, we prove that  = A when A is a von Neumann algebra. We also derive from our characterization new proofs of previously known results, namely Feldman...
The cohomology ring of free loop spaces.
The Connes-Kasparov conjecture for almost connected groups and for linear -adic groups
Let G be a locally compact group with cocompact connected component. We prove that the assembly map from the topological K-theory of G to the K-theory of the reduced C*-algebra of G is an isomorphism. The same is shown for the groups of k-rational points of any linear algebraic group over a local field k of characteristic zero.
The continuity of multiplication for two topologies associated with a semifinite trace on von Neumann algebra.
The correspondence associated to an inner completely positive map.
The cyclic homology of affine algebras.
The cyclic homology of crossed product algebras.