We prove that, for 1 < p = q < ∞, there does not exist any coarse Lipschitz embedding between the two James spaces Jp and Jq, and that, for 1 < p < q < ∞ and 1 < r < ∞ such that r / ∈ {p, q}, Jr does not coarse Lipschitz embed into Jp ⊕ Jq.
We are interested in a sufficient condition given in [19] 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 show in this paper that, for two infinite dimensional Banach spaces X and Y , if X is finitely crudely representable in the finite codimensional subspaces of Y , then any proper subset of X almost bi-Lipschitz embeds into Y .
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