Small Subspaces of L_p

R. Haydon; E. Odell; Th. Schlumprecht

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arXiv · 0711.3919

Small Subspaces of L_p

R. Haydon·E. Odell·Th. Schlumprecht

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Abstract

We prove that if $X$ is a subspace of $L_p$ $(2<p<\infty)$, then either $X$ embeds isomorphically into $\ell_p \oplus \ell_2$ or $X$ contains a subspace $Y,$ which is isomorphic to $\ell_p(\ell_2)$. We also give an intrinsic characterization of when $X$ embeds into $\ell_p \oplus \ell_2$ in terms of weakly null trees in $X$ or, equivalently, in terms of the "infinite asymptotic game" played in $X$. This solves problems concerning small subspaces of $L_p$ originating in the 1970's. The techniques used were developed over several decades, the most recent being that of weakly null trees developed in the 2000's.

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BibTeX RIS

R. Haydon, E. Odell, Th. Schlumprecht. 2010-03-05. Small Subspaces of L_p. https://arxiv.org/abs/0711.3919

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