Isometric actions on <i>L</i><sub><i>p</i></sub>-spaces: dependence on the value of <i>p</i>
Isometric actions on <i>L</i><sub><i>p</i></sub>-spaces: dependence on the value of <i>p</i>
Answering a question by Chatterjiā€“DruÅ£uā€“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 ( $0< p<\infty$ ) with unbounded orbits if and only if $p \geq ā€¦