Généralisation d'un théorème de Haagerup

• Autorzy: Ferdaous Kellil , Guy Rousseau
• Języki publikacji: FR EN

Abstrakty

EN

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.

Kategorie tematyczne

• 47A30: Norms (inequalities, more than one norm, etc.)
• 20E08: Groups acting on trees
• 43A85: Analysis on homogeneous spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2005
• Tom: 168
• Numer: 3
• Strony: 217-227

Daty

wydano

2005

Twórcy

autor

Ferdaous Kellil

• Département de Mathématiques, Faculté des Sciences de Monastir, 5000 Monastir, Tunisie

autor

Guy Rousseau

• Institut Elie Cartan, Unité mixte de Recherche 7502, Université Henri Poincaré Nancy 1, B.P. 239, 54506 Vandœuvre-lès-Nancy, France

Identyfikatory

DOI

10.4064/sm168-3-3