Maximal \(\ell_p^n\)-Structures in Spaces with Extremal Parameters
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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):46-06 46B07 52-06 60-06
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