Subspaces of $L_p$ that embed into $L_p(\mu)$ with $\mu$ finite

William B. Johnson; Gideon Schechtman

Subspaces of $L_p$ that embed into $L_p(\mu)$ with $\mu$ finite

Functional Analysis 2013-01-18 v1

Authors: William B. Johnson , Gideon Schechtman

Abstract

Enflo and Rosenthal proved that $\ell_p(\aleph_1)$ , $1 < p < 2$ , does not (isomorphically) embed into $L_p(\mu)$ with $\mu$ a finite measure. We prove that if $X$ is a subspace of an $L_p$ space, $1< p < 2$ , and $\ell_p(\aleph_1)$ does not embed into $X$ , then $X$ embeds into $L_p(\mu)$ for some finite measure $\mu$ .

Keywords

$l_p$ spaces isomorphic embedding finite measure subspaces enflo-rosenthal theorem banach space theory

Cite

@article{arxiv.1301.4086,
  title  = {Subspaces of $L_p$ that embed into $L_p(\mu)$ with $\mu$ finite},
  author = {William B. Johnson and Gideon Schechtman},
  journal= {arXiv preprint arXiv:1301.4086},
  year   = {2013}
}

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