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General construction of non-dense disjoint iteration groups on the circle

Krzysztof Ciepliński (2005)

Czechoslovak Mathematical Journal

Let = { F v 𝕊 1 𝕊 1 , v V } be a disjoint iteration group on the unit circle 𝕊 1 , that is a family of homeomorphisms such that F v 1 F v 2 = F v 1 + v 2 for v 1 , v 2 V and each F v either is the identity mapping or has no fixed point ( ( V , + ) is a 2 -divisible nontrivial Abelian group). Denote by L the set of all cluster points of { F v ( z ) , v V } for z 𝕊 1 . In this paper we give a general construction of disjoint iteration groups for which L 𝕊 1 .

Généralisation d'un théorème de Haagerup

Ferdaous Kellil, Guy Rousseau (2005)

Studia Mathematica

Let G be a group of automorphisms of a tree X (with set of vertices S) and H a kernel on S × S invariant under the action of G. We want to give an estimate of the l r -operator norm (1 ≤ r ≤ 2) of the operator associated to H in terms of a norm for H. This was obtained by U. Haagerup when G is the free group acting simply transitively on a homogeneous tree. Our result is valid when X is a locally finite tree and one of the orbits of G is the set of vertices at even distance from a given vertex; a technical...

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