26 Mar
2013
26 Mar
'13
10:51 a.m.
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
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