Radial functions on free groups and a decomposition of the regular representation into irreducible components.
Räume primitiver Ideale von Gruppenalgebren.
Regulär Representations of Unimodular Groups.
Relative Commutant of a von Neumann Algebra in Its Crossed Product by a Group Action.
Semigroup crossed products and Hecke algebras arising from number fields.
Sets of p-multiplicity in locally compact groups
We initiate the study of sets of p-multiplicity in locally compact groups and their operator versions. We show that a closed subset E of a second countable locally compact group G is a set of p-multiplicity if and only if is a set of operator p-multiplicity. We exhibit examples of sets of p-multiplicity, establish preservation properties for unions and direct products, and prove a p-version of the Stone-von Neumann Theorem.
Simple quotients of group -algebras for two step nilpotent groups and connected Lie groups
Some aspects of harmonic analysis on free groups
Some groups whose reduced -algebra is simple
Some remarks on C*-bigebras and duality.
Spectral Pairs in Cartesian Coordinates.
Spectral subspaces and non-commutative Hilbert transforms
Let G be a locally compact abelian group and ℳ be a semifinite von Neumann algebra with a faithful semifinite normal trace τ. We study Hilbert transforms associated with G-flows on ℳ and closed semigroups Σ of Ĝ satisfying the condition Σ ∪ (-Σ) = Ĝ. We prove that Hilbert transforms on such closed semigroups satisfy a weak-type estimate and can be extended as linear maps from L¹(ℳ,τ) into . As an application, we obtain a Matsaev-type result for p = 1: if x is a quasi-nilpotent compact operator...
Spectrum of commutative Banach algebras and isomorphism of C*-algebras related to locally compact groups
Let A be a semisimple commutative regular tauberian Banach algebra with spectrum . In this paper, we study the norm spectra of elements of and present some applications. In particular, we characterize the discreteness of in terms of norm spectra. The algebra A is said to have property (S) if, for all , φ has a nonempty norm spectrum. For a locally compact group G, let denote the C*-algebra generated by left translation operators on and denote the discrete group G. We prove that the Fourier...
Stabilité du comportement des marches aléatoires sur un groupe localement compact
Dans cet article nous démontrons un théorème de stabilité des probabilités de retour sur un groupe localement compact unimodulaire, séparable et compactement engendré. Nous démontrons que le comportement asymptotique de F*(2n)(e) ne dépend pas de la densité F sous des hypothèses naturelles. A titre d’exemple nous établissons que la probabilité de retour sur une large classe de groupes résolubles se comporte comme exp(−n1/3).
Strong Morita Equivalence of Certain Transformation Group C*-Algebras.
Structure de certaines -algèbres associées aux réseaux de
En utilisant la structure infinitésimale des représentations unitaires irréductibles de , nous donnons une description complète de certaines - algèbres associées aux réseaux de , répondant ainsi à certaines questions de Bekka–de La Harpe–Valette.
Subhypergroups and Normal Subgroups.
Sur le type du produit croisé d'une algèbre de von Neumann par un groupe localement compact
Sur l'espace de Banach engendré par les coefficients d'une représentation unitaire
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.