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Généralisation d'un théorème de Haagerup

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Kellil F., Rousseau G.

Studia Mathematica

2005

tom 168

nr 3

217-227

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 hypothesis, always true when G is discrete, is also assumed. As an application we prove the invertibility of an $l^{r}$-operator on S.

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1 Studia Mathematica

1 Kellil F.

1 Rousseau G.

1 2005

Wyniki wyszukiwania

Généralisation d'un théorème de Haagerup