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Power boundedness in Banach algebras associated with locally compact groups

E. Kaniuth, A. T. Lau, A. Ülger (2014)

Studia Mathematica

Let G be a locally compact group and B(G) the Fourier-Stieltjes algebra of G. Pursuing our investigations of power bounded elements in B(G), we study the extension property for power bounded elements and discuss the structure of closed sets in the coset ring of G which appear as 1-sets of power bounded elements. We also show that L¹-algebras of noncompact motion groups and of noncompact IN-groups with polynomial growth do not share the so-called power boundedness property. Finally, we give a characterization...

Proper cocycles and weak forms of amenability

Paul Jolissaint (2015)

Colloquium Mathematicae

Let G and H be locally compact, second countable groups. Assume that G acts in a measure class preserving way on a standard space (X,μ) such that L ∞ ( X , μ ) has an invariant mean and that there is a Borel cocycle α: G × X → H which is proper in the sense of Jolissaint (2000) and Knudby (2014). We show that if H has one of the three properties: Haagerup property (a-T-menability), weak amenability or weak Haagerup property, then so does G. In particular, we show that if Γ and Δ are measure equivalent discrete...

Property (T) and A ¯ 2 groups

Donald I. Cartwright, Wojciech Młotkowski, Tim Steger (1994)

Annales de l'institut Fourier

We show that each group Γ in a class of finitely generated groups introduced in [2] and [3] has Kazhdan’s property (T), and calculate the exact Kazhdan constant of Γ with respect to its natural set of generators. These are the first infinite groups shown to have property (T) without making essential use of the theory of representations of linear groups, and the first infinite groups with property (T) for which the exact Kazhdan constant has been calculated. These groups therefore provide answers...

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