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Factorizations of natural embeddings of \(\ell^ n_ p\) into \(L_ r\). II. (English) Zbl 0764.46018

This paper improves results from part I [Studia Math. 89, No. 1, 79-103 (1988; Zbl 0671.46009)] by the same authors. From the abstract:
1. If \(T\) is a “natural” embedding of \(\ell_ 2^ n\) 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 1, \(u\) well-preserves a copy of \(\ell_ 1^ k\) with \(k\) exponential in \(n\).
2. Any norm 1 operator from a \(C(K)\) space which well-preserves a copy of \(\ell_ 2^ n\) also well-preserves a copy of \(\ell_ \infty^ k\) with \(k\) exponential in \(n\).

MSC:

46B25 Classical Banach spaces in the general theory
47A68 Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators

Citations:

Zbl 0671.46009
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