Algèbres de Fourier associées à une algèbre de Kac.
Almost L2 matrix coefficients.
Almost periodic compactifications of group extensions
Let and be groups and let be an extension of by . Given a property of group compactifications, one can ask whether there exist compactifications and of and such that the universal -compactification of is canonically isomorphic to an extension of by . We prove a theorem which gives necessary and sufficient conditions for this to occur for general properties and then apply this result to the almost periodic and weakly almost periodic compactifications of .
Amenability and coamenability of algebraic quantum groups.
Amenability, unimodularity, and the spectral radius of random walks on finite graphs.
Amenable hyperbolic groups
We give a complete characterization of the locally compact groups that are non elementary Gromov-hyperbolic and amenable. They coincide with the class of mapping tori of discrete or continuous one-parameter groups of compacting automorphisms. We moreover give a description of all Gromov-hyperbolic locally compact groups with a cocompact amenable subgroup: modulo a compact normal subgroup, these turn out to be either rank one simple Lie groups, or automorphism groups of semiregular trees acting doubly...
Amenable unitary representations of locally compact groups.
An analytic series of irreducible representations of the free group
Let be a free group on generators. We construct the series of uniformly bounded representations of acting on the common Hilbert space, depending analytically on the complex parameter z, , such that each representation is irreducible. If is real or then is unitary; in other cases cannot be made unitary. For representations and are congruent modulo compact operators.
An example of a generalized completely continuous representation of a locally compact group
There is constructed a compactly generated, separable, locally compact group G and a continuous irreducible unitary representation π of G such that the image π(C*(G)) of the group C*-algebra contains the algebra of compact operators, while the image of the -group algebra does not containany nonzero compact operator. The group G is a semidirect product of a metabelian discrete group and a “generalized Heisenberg group”.
An Example of a Non Nuclear C*-Algebra, which has the Metric Approximation Property.
An Exposition of the Connection between Limit-Periodic Potentials and Profinite Groups
We classify the hulls of different limit-periodic potentials and show that the hull of a limit-periodic potential is a procyclic group. We describe how limit-periodic potentials can be generated from a procyclic group and answer arising questions. As an expository paper, we discuss the connection between limit-periodic potentials and profinite groups as completely as possible and review some recent results on Schrödinger operators obtained in this...
An Imprimitivity Theorem for Hypergroups.
An invariant for finitely presented ...G-modules.
An -criterion of amenability for a locally compact group.
Analyse harmonique hyperbolique : représentations et contractions des groupes
Analyse Harmonique sur les groupes de Heisenberg généralisés.
Analysis on a class of Banach algebras with applications to harmonic analysis on locally compact groups and semigroups
Applications de la p-induction en analyse harmonique.
Approximate diagonals and Følner conditions for amenable group and semigroup algebras
We study the relationship between the classical invariance properties of amenable locally compact groups G and the approximate diagonals possessed by their associated group algebras L¹(G). From the existence of a weak form of approximate diagonal for L¹(G) we provide a direct proof that G is amenable. Conversely, we give a formula for constructing a strong form of approximate diagonal for any amenable locally compact group. In particular we have a new proof of Johnson's Theorem: A locally compact...
Arcs in Locally compact Groups