Coarse Lipschitz embeddings of James spaces

TL;DR

This paper proves the non-existence of coarse Lipschitz embeddings between different James spaces and their direct sums, revealing structural limitations in their metric geometry.

Contribution

It establishes new non-embedding results for James spaces, showing they cannot be coarsely Lipschitz embedded into each other or their sums under certain conditions.

Findings

No coarse Lipschitz embedding between J_p and J_q for p ≠ q.

J_r does not embed into J_p ⊕ J_q when r is distinct from p and q.

Results clarify the geometric rigidity of James spaces.

Abstract

We prove that, for $1 < p \neq q < \infty$, 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 $J_p \oplus J_q$.