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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Remarks about Schlumprecht space


Authors: Denka Kutzarova and Pei-Kee Lin
Journal: Proc. Amer. Math. Soc. 128 (2000), 2059-2068
MSC (2000): Primary 46B20, 46B45
Published electronically: December 8, 1999
MathSciNet review: 1654081
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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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Additional Information

Denka Kutzarova
Affiliation: Institute of Mathematics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria
Address at time of publication: Department of Mathematics, University of South Carolina, Columbia, South Carolina
Email: denka@math.sc.edu

Pei-Kee Lin
Affiliation: Department of Mathematics, University of Memphis, Memphis, Tennessee 38152
Email: linpk@msci.memphis.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05248-X
PII: S 0002-9939(99)05248-X
Received by editor(s): August 3, 1998
Received by editor(s) in revised form: August 27, 1998
Published electronically: December 8, 1999
Additional Notes: Part of this paper was done when the second author visited the University of Texas at Austin and was completed when the first author participated in the Workshop in Linear Analysis and Probability Theory at Texas A&M University, 1998. Both authors would like to thank E. Odell and Th. Schlumprecht for their valuable discussions
Communicated by: Dale Alspach
Article copyright: © Copyright 2000 American Mathematical Society