Coarse embeddings into superstable spaces
Abstract
Krivine and Maurey proved in 1981 that every stable Banach space contains almost isometric copies of p, 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 p, 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 p, 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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