Arcs in Locally compact Groups
Arens Semi-Regular Banach Algebras.
Arithmetic aspect of operator algebras
Asymptotisch gleichverteilte Netze von Wahrscheinlichkeitsmassen auf lokalkompakten Gruppen
Automatic continuity of operators commuting with translations
Let and be representations of a topological group G on Banach spaces X and Y, respectively. We investigate the continuity of the linear operators Φ: X → Y with the property that for each t ∈ G in terms of the invariant vectors in Y and the automatic continuity of the invariant linear functionals on X.
Automatic Continuity over Moore Groups.
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.
Automorphismen nilpotenter proendlicher Gruppen.
Averages of unitary representations and weak mixing of random walks
Let S be a locally compact (σ-compact) group or semigroup, and let T(t) be a continuous representation of S by contractions in a Banach space X. For a regular probability μ on S, we study the convergence of the powers of the μ-average Ux = ʃ T(t)xdμ(t). Our main results for random walks on a group G are: (i) The following are equivalent for an adapted regular probability on G: μ is strictly aperiodic; converges weakly for every continuous unitary representation of G; U is weakly mixing for any...
Banach algebras associated with Laplacians on solvable Lie groups and injectivity of the Harish-Chandra transform
For any connected Lie group G and any Laplacian Λ = X²₁ + ⋯ + X²ₙ ∈ 𝔘𝔤 (X₁,...,Xₙ being a basis of 𝔤) one can define the commutant 𝔅 = 𝔅(Λ) of Λ in the convolution algebra ℒ¹(G) as well as the commutant ℭ(Λ) in the group C*-algebra C*(G). Both are involutive Banach algebras. We study these algebras in the case of a "distinguished Laplacian" on the "Iwasawa part AN" of a semisimple Lie group. One obtains a fairly good description of these algebras by objects derived from the semisimple group....
Banach Convolution Algebras of Functions II.
Beurling algebras on locally compact groups, tensor products, and multipliers
Beurling-Figà-Talamanca-Herz algebras
For a locally compact group G and p ∈ (1,∞), we define and study the Beurling-Figà-Talamanca-Herz algebras . For p = 2 and abelian G, these are precisely the Beurling algebras on the dual group Ĝ. For p = 2 and compact G, our approach subsumes an earlier one by H. H. Lee and E. Samei. The key to our approach is not to define Beurling algebras through weights, i.e., possibly unbounded continuous functions, but rather through their inverses, which are bounded continuous functions. We prove that...
Bitwisted Burnside-Frobenius theorem and Dehn conjugacy problem
It is proved for Abelian groups that the Reidemeister coincidence number of two endomorphisms ϕ and ψ is equal to the number of coincidence points of ϕ̂ and ψ̂ on the unitary dual, if the Reidemeister number is finite. An affirmative answer to the bitwisted Dehn conjugacy problem for almost polycyclic groups is obtained. Finally, we explain why the Reidemeister numbers are always infinite for injective endomorphisms of Baumslag-Solitar groups.
Block additive functions on the Gaussian integers
Bounded orbits of flows on homogeneous spaces.
Capacité et théorie du renouvellement. I
Capacités invariantes extrémales
On étudie certains cônes de mesures sur un espace localement compact, qui sont invariantes par l’action continue d’un groupe localement compact , cette étude étant centrée sur les génératrices extrémales de ces cônes. On dégage d’abord un type très simple d’action continue où l’on décrit complètement la situation. On dégage ensuite une classe d’actions (contenant par exemple l’action de shift de Bernoulli sur ) qui ne sont pas du type précédent, et que l’on étudie en grand détail. Le résultat...
Center of Group Algebras.
Centered operators