Isometric actions on Lp-spaces: dependence on the value of p - CNRS - Centre national de la recherche scientifique Accéder directement au contenu
Article Dans Une Revue Compositio Mathematica Année : 2023

Isometric actions on Lp-spaces: dependence on the value of p

Résumé

Answering a question by Chatterji--Dru\c{t}u--Haglund, we prove that, for every locally compact group $G$, there exists a critical constant $p_G \in [0,\infty]$ such that $G$ admits a continuous affine isometric action on an $L_p$ space ($02$. We also prove the stability of this critical constant $p_G$ under $L_p$ measure equivalence, answering a question of Fisher. We use this to show that for every connected semisimple Lie group $G$ and for every lattice $\Gamma < G$, we have $p_\Gamma=p_G$.

Dates et versions

hal-02955585 , version 1 (02-10-2020)

Identifiants

Citer

Amine Marrakchi, Mikael de la Salle. Isometric actions on Lp-spaces: dependence on the value of p. Compositio Mathematica, 2023, 159 (6), pp.1300-1313. ⟨10.1112/s0010437x23007121⟩. ⟨hal-02955585⟩
37 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More