Remarks about Schlumprecht space

Abstract

We prove that Schlumprecht space $S$ is isomorphic to $({\sum }_{k=1}^{\infty }\oplus {\ell }_{i}nft{y}^{n_k}{)}_S$ for any sequence of integers $(n_k)$. We also show that every complemented subspace of $S$ which has some subsymmetric basis, is isomorphic to $S$.