ℓ1-Spreading models in mixed tsirelson space

Abstract

Suppose that (Fn)n=1 ∞is a sequence of regular families of finite subsets of ℕ and (θn) n=1 ∞ is a nonincreasing null sequence in (0, 1). The mixed Tsirelson space T[(θn,Fn)n=1 ∞] is the completion of c00 with respect to the implicitly defined norm

x

= max{

x

c0, sup sup θn {

Eix

}, where the last supremum is taken over all sequences (Ei)i=1 k in [ℕ]