Corpus ID: 210064240

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

@article{Marrakchi2020IsometricAO,
  title={Isometric actions on Lp-spaces: dependence on the value of p},
  author={A. Marrakchi and M. D. L. Salle},
  journal={arXiv: Group Theory},
  year={2020}
}
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 ($0 2$. 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 $p_\Gamma=p_G$. 
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