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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Espaces $l^{p}$ dans les sous-espaces de $L^{1}$
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by S. Guerre and M. Levy
Trans. Amer. Math. Soc. 279 (1983), 611-616
DOI: https://doi.org/10.1090/S0002-9947-1983-0709571-3

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.
References
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Bibliographic Information
  • © Copyright 1983 American Mathematical Society
  • 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