Lattices in amenable groups

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Amenable Groups

Throughout we let Γ be a discrete group. For f : Γ → C and each s ∈ Γ we define the left translation action by (s.f)(t) = f(s−1t). Definition 1.1. A group Γ is amenable is there exists a state μ on l∞(Γ) which is invariant under the left translation action: for all s ∈ Γ and f ∈ l∞(Γ), μ(s.f) = μ(f). Example 1.2. Finite groups are amenable: take the state which sends χ{s} to 1 |Γ| for each s ∈ ...

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ژورنال

عنوان ژورنال: Fundamenta Mathematicae

سال: 2019

ISSN: 0016-2736,1730-6329

DOI: 10.4064/fm572-9-2018