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Factorizations of natural embeddings of l_p^n int L_r

Tadek Figiel·William B. Johnson·Gideon Schechtman
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Abstract

This is a continuation of the paper [FJS] with a similar title. Several results from there are strengthened, in particular: 1. If T is a "natural" embedding of l_2^n into L_1 then, for any well-bounded factorization of T through an L_1 space in the form T=uv with v of norm one, u well-preserves a copy of l_1^k with k exponential in n. 2. Any norm one operator from a C(K) space which well-preserves a copy of l_2^n also well-preserves a copy of l_{\infty}^k with k exponential in n. As an application of these and other results we show the existence, for any n, of an n-dimensional space which well-embeds into a space with an unconditional basis only if the latter contains a copy of l_{\infty}^k with k exponential in n.

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Tadek Figiel, William B. Johnson, Gideon Schechtman. 1992-01-06. Factorizations of natural embeddings of l_p^n int L_r. https://arxiv.org/abs/math/9201202

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