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Remarks about Schlumprecht space

Authors:	Denka Kutzarova Pei-Kee Lin

Institution:	Institute of Mathematics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria ; Department of Mathematics, University of Memphis, Memphis, Tennessee 38152

Abstract:	Let $\mathbf S$ denote the Schlumprecht space. We prove that (1) $\ell _\infty$ is finitely disjointly representable in $\mathbf S$ ; (2) $\mathbf S$ contains an $\ell _1$ -spreading model; (3) for any sequence of natural numbers, $\mathbf S$ is isomorphic to the space $(\sum _{k=1}^\infty\oplus \ell _\infty^{n_k})_{\mathbf S}$ .

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