Factorizations of natural embeddings oflpnintoLr. II

Tadeusz Figiel, William Johnson, Gideon Schechtman
1991 Pacific Journal of Mathematics  
This is a continuation of the paper by Figiel, Johnson and Schechtman with a similar title. Several results from there are strengthened, in particular: 1. If T is a "natural" embedding of lζ into L\ then, for any well-bounded factorization of T through an L\ space in the form T -uv with υ of norm one, u well-preserves a copy of /f with k exponential in n . 2. Any norm one operator from a C(K) space which well-preserves a copy of /£ also well-preserves a copy of /£, with k exponential in n . As
more » ... n application of these and other results we show the existence, for any n , of an π-dimensional space which well-embeds into a space with an unconditional basis only if the latter contains a copy of /£> with k exponential in n .
doi:10.2140/pjm.1991.150.261 fatcat:ufmwfd52ird7rgduh3yew4x7dq