Diamond graphs and super-reflexivity
نویسندگان
چکیده
The main result is that a Banach space X is not super-reflexive if and only if the diamond graphs Dn Lipschitz embed into X with distortions independent of n. One of the consequences of that and previously known results is that dimension reduction a-la Johnson–Lindenstrauss fails in any non super reflexive space with non trivial type. We also introduce the concept of Lipschitz (p, r)-summing map and prove that every Lipschitz mapping is Lipschitz (p, r)-summing for every 1 ≤ r < p.
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