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 -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 -operator on S.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm168-3-3,
author = {Ferdaous Kellil and Guy Rousseau},
title = {G\'en\'eralisation d'un th\'eor\`eme de Haagerup},
journal = {Studia Mathematica},
volume = {166},
year = {2005},
pages = {217-227},
zbl = {1073.43006},
language = {fra},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm168-3-3}
}
Ferdaous Kellil; Guy Rousseau. Généralisation d'un théorème de Haagerup. Studia Mathematica, Tome 166 (2005) pp. 217-227. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm168-3-3/