Remarks about Schlumprecht space

Kutzarova, Denka; Lin, Pei-Kee

doi:10.1090/S0002-9939-99-05248-X

Remarks about Schlumprecht space
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by Denka Kutzarova and Pei-Kee Lin

Proc. Amer. Math. Soc. 128 (2000), 2059-2068

DOI: https://doi.org/10.1090/S0002-9939-99-05248-X

Published electronically: December 8, 1999

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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 $(n_k)$ 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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