Coarse Lipschitz embeddings of James spaces

Abstract

We prove that, for $1<p\ne q<\infty$, there does not exist any coarse Lipschitz embedding between the two James spaces $J_p$ and $J_q$, and that, for $1<p<q<\infty$ and $1<r<\infty$ such that $r\notin \{p,q\}$, $J_r$ does not coarse Lipschitz embed into $J_p\oplus J_q$.