Abstract
We prove that every n-dimensional normed space with a type p < 2, cotype 2, and (asymptotically) extremal Euclidean distance has a quotient of a subspace, which is well isomorphic to \(\ell_p^k\) and with the dimension k almost proportional to n. A structural result of a similar nature is also proved for a sequence of vectors with extremal Rademacher average inside a space of type p. The proofs are based on new results on restricted invertibility of operators from \(\ell_r^n\) into a normed space X with either type r or cotype r.Mathematics Subject Classification (2000):46-0646B0752-06 60-06
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