[Banach] Abstract of a paper by Gideon Schechtman

This is an announcement for the paper "Matrix subspaces of $L_1$" by Gideon Schechtman.

Abstract: If $E={e_i}$ and $F={f_i}$ are two 1-unconditional basic sequences in $L_1$ with $E$ $r$-concave and $F$ $p$-convex, for some $1\le r<p\le 2$, then the space of matrices ${a_{i,j}}$ with norm $|{a_{i,j}}|_{E(F)}=\big|\sum_k |\sum_l a_{k,l}f_l|e_k\big|$ embeds into $L_1$. This generalizes a recent result of Prochno and Sch"utt.

Archive classification: math.FA

Mathematics Subject Classification: 46E30, 46B45, 46B15

Submitted from: gideon@weizmann.ac.il

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

http://front.math.ucdavis.edu/1303.4590

or

http://arXiv.org/abs/1303.4590