Abstract
Krivine and Maurey proved in 1981 that every stable Banach space contains almost isometric copies of ℓp, for some p ∊ [1, ∞). In 1983, Raynaud showed that if a Banach space uniformly embeds into a superstable Banach space, then X must contain an isomorphic copy of ℓp, for some p ∊ [1, ∞). In these notes, we show that if a Banach space coarsely embeds into a superstable Banach space, then X has a spreading model isomorphic to ℓp, for some p ∊ [1, ∞). In particular, we obtain that there exist reflexive Banach spaces which do not coarsely embed into any superstable Banach space.
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Braga, B.d., Swift, A.T. Coarse embeddings into superstable spaces. Isr. J. Math. 232, 1–39 (2019). https://doi.org/10.1007/s11856-019-1862-x
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DOI: https://doi.org/10.1007/s11856-019-1862-x