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Proposition 12 (Ceccherini-Silberstein, Machi and Scarabotti [7]) Let G be an amenable group and let A be a CA on G.
Lemma 19 (Step 1 in proof of [7, Theorem 3]) Let G be a finitely generated amenable group, q [greater than or equal to] 2, and n > r > 0.
Proposition 20 Let G be a finitely generated amenable group and let A = <Q, [D.
Let [pi]: G [right arrow] O(H) be an ergodic orthogonal representation of a finitely generated amenable group G, and let b: G [right arrow] H be a 1-cocycle associated to [pi].
Let G be finitely generated amenable group admitting a controlled Folner sequence.
Let G be an amenable group, and let f: G [right arrow] V be a large scale lipschitz map.
Matui, [12], produces the first examples of infinite simple finitely generated amenable groups.
5]), as well as all elementary amenable groups with exponential growth (by [4] such groups contain a free subsemigroup).
We show that the Fourier algebra of every locally compact amenable group has the property (B) completely.
Let G be a locally compact amenable group and suppose that B is a commutative C*-algebra or a matrix space.
Let G be an inner amenable group and let A be a Borel subset of G.
A good deal of attention was paid to the study of inner amenable groups.
If G is an infinite amenable group and there is a H-set Y such that the H-action is amenable and the action of A on Y is free, then [G.
As corollaries, the amalgamated free product of an infinite amenable group and a residually finite group over a finite subgroup (for instance [SL.
Willis, Weak convergence is not strong for amenable groups, Canadian Mathematical Bulletin, 44 (2)(2001), 231-241.