[Banach] Abstract of a paper by William B. Johnson and Gideon Schechtman

This is an announcement for the paper "Subspaces of $L_p$ that embed into $L_p(\mu)$ with $\mu$ finite" by William B. Johnson and 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 $\mu$.

Archive classification: math.FA

Mathematics Subject Classification: 46E30, 46B26, 46B03

Submitted from: gideon@weizmann.ac.il

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1301.4086

or

http://arXiv.org/abs/1301.4086