We prove that the convex intersection bodies are isomorphically equivalent to unit balls of subspaces of Lqfor each q ∈ (0, 1). This is done by extending to negative values of p the factorization theorem of Maurey and Nikishin which states that for any 0 < p < q < 1 every Banach subspace of Lpis isomorphic to a subspace of Lq. © 2004 Elsevier Inc. All rights reserved.
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