A Characterization of SIN-Groups.
A concavity property for the measure of product sets in groups
Let G be a connected locally compact group with a left invariant Haar measure μ. We prove that the function ξ(x) = inf μ̅(AB): μ(A) = x is concave for any fixed bounded set B ⊂ G. This is used to give a new proof of Kemperman’s inequality for unimodular G.
A generalized universal complexification for compact groups.
A non-seperable measureable choice principle related to induced representations.
A Note on Reduced Duals of Certain Locally Compact Groups.
A note on the automorphisms of a WAP-compactification.
A note on the WAP-compactification of groups.
A Short Proof of a Classical Covering Lemma.
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, 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...
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
Asymptotisch gleichverteilte Netze von Wahrscheinlichkeitsmassen auf lokalkompakten Gruppen
Automorphism groups of right-angled buildings: simplicity and local splittings
We show that the group of type-preserving automorphisms of any irreducible semiregular thick right-angled building is abstractly simple. When the building is locally finite, this gives a large family of compactly generated abstractly simple locally compact groups. Specialising to appropriate cases, we obtain examples of such simple groups that are locally indecomposable, but have locally normal subgroups decomposing non-trivially as direct products, all of whose factors are locally normal.
Capacité et théorie du renouvellement. I
Chu-Dualität und zwei Klassen maximal fastperiodischer Gruppen.
Coherent pair of extensions of locally compact groups
Compactness conditions in topological groups.
Concentration Functions and a Class of Non-Compact Groups.