منابع مشابه
Some extremely amenable groups
A topological group G is extremely amenable if every continuous action of G on a compact space has a fixed point. Using the concentration of measure techniques developed by Gromov and Milman, we prove that the group of automorphisms of a Lebesgue space with a non-atomic measure is extremely amenable with the weak topology but not with the uniform one. Strengthening a de la Harpe’s result, we sh...
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This is a preliminary note containing the proof that every countable non-amenable group admits continuum many orbit inequivalent free, measure preserving, ergodic actions on a standard Borel space with probability measure. 1. Summary and Notation Let Γ1 y α1 (X1, μ1),Γ2 y α2 (X2, μ2) be Borel measure preserving actions. α1 and α2 are orbit equivalent if there exist conull subsets A1 ⊂ X1, A2 ⊂ ...
متن کاملNon-elementary amenable subgroups of automata groups
We consider groups of automorphisms of locally finite trees, and give conditions on its subgroups that imply that they are not elementary amenable. This covers all known examples of groups that are not elementary amenable and act on the trees: groups of intermediate growths and Basilica group, by giving a more straightforward proof. Moreover, we deduce that all finitely generated branch groups ...
متن کاملAmenable 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 ∈ ...
متن کاملAre Unitarizable Groups Amenable?
We give a new formulation of some of our recent results on the following problem: if all uniformly bounded representations on a discrete group G are similar to unitary ones, is the group amenable? In §5, we give a new proof of Haagerup's theorem that, on non-commutative free groups, there are Herz-Schur multipliers that are not coefficients of uniformly bounded representations. We actually prov...
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ژورنال
عنوان ژورنال: Publicacions Matemàtiques
سال: 2012
ISSN: 0214-1493
DOI: 10.5565/publmat_56112_09