Espaces 𝑙^{𝑝} dans les sous-espaces de 𝐿¹

Guerre, S.; Levy, M.

doi:10.1090/S0002-9947-1983-0709571-3

Espaces $l^{p}$ dans les sous-espaces de $L^{1}$
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by S. Guerre and M. Levy PDF

Trans. Amer. Math. Soc. 279 (1983), 611-616 Request permission

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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