On impossible extensions of Krivine's Theorem

Abstract

We give examples of two Banach spaces. One Banach space has no spreading model which contains ${\ell }_p$ ($1\le p<\infty$) or $c_0$. The other space has an unconditional basis for which ${\ell }_p$ ($1\le p<\infty$) and $c_0$ are block finitely represented in all block bases.