Figiel, T.; Johnson, W. B.; Schechtman, G. Factorizations of natural embeddings of \(\ell^ n_ p\) into \(L_ r\). II. (English) Zbl 0764.46018 Pac. J. Math. 150, No. 2, 261-277 (1991). 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 \(n\). Reviewer: J.P.Holmes (Auburn) Cited in 1 Document MSC: 46B25 Classical Banach spaces in the general theory 47A68 Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators Keywords:factorizations; embeddings Citations:Zbl 0671.46009 PDFBibTeX XMLCite \textit{T. Figiel} et al., Pac. J. Math. 150, No. 2, 261--277 (1991; Zbl 0764.46018) Full Text: DOI