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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Espaces $ l\sp{p}$ dans les sous-espaces de $ L\sp{1}$


Authors: S. Guerre and M. Levy
Journal: Trans. Amer. Math. Soc. 279 (1983), 611-616
MSC: Primary 46E30
DOI: https://doi.org/10.1090/S0002-9947-1983-0709571-3
MathSciNet review: 709571
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Abstract: It is shown that every subspace $ E$ of $ {L^1}$ contains a subspace isomorphic to $ {l^{p(E)}}$, where $ p(E)$ is the upper bound of the set of real $ p$'s such that $ E$ is of type $ p$-Rademacher. As $ p(E)$ is also the upper bound of the set of real $ p$'s such that $ E$ embeds into $ {L^p}$, this result answers a question of H. P. Rosenthal.

The proof uses the theory of stable Banach spaces developed by J. L. Krivine and B. Maurey.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1983-0709571-3
Keywords: $ {L^1}$-spaces, $ {l^p}$-subspaces of $ {L^1}$, stable Banach spaces, ultrapowers
Article copyright: © Copyright 1983 American Mathematical Society