arXiv subjects
Publications and source records attributed to François Netillard.
Let X and Y be two infinite-dimensional Banach spaces. If X is crudely finitely representable in every finite-codimensional subspace of Y, then any proper subset of X almost bi-Lipschitz embeds into Y, in a sense quite close to that of F. Baudier and G. Lancien. This is an extension of a result proved by M.I. Ostrovskii for locally finite subsets.
We are interested in a sufficient condition given in an article by P. Lefèvre, É. Matheron and A. Primot to obtain the Blum-Hanson Property and we then partially answer two questions asked in this same article on other possible conditions to have this property for a separable Banach space.
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 $J_p \oplus J_q$.