This is an announcement for the paper "Ordinal indices of small subspaces of $L_p$" by S Dutta and D Khurana.

Abstract: We calculate ordinal $L_p$ index defined in "An ordinal L_p index for Banach spaces with an application to complemented subspaces of L_p" authored by J. Bourgain, H. P. Rosenthal and G. Schechtman, for Rosenthal's space $X_p$, $\ell_p$ and $\ell_2$. We show a subspace of $L_p$ $(2 < p < \infty)$ non isomorphic to $\ell_2$ embeds in $\ell_p$ if and only if its ordinal index is minimum possible. We also give a sufficient condition for a $\mathcal{L}_p$ subspace of $\ell_p\oplus\ell_2$ to be isomorphic to $X_p$.

Archive classification: math.FA

Submitted from: divyakhurana11@gmail.com

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

http://front.math.ucdavis.edu/1409.2330

or

http://arXiv.org/abs/1409.2330