Matrix subspaces of $L_1$
Volume 215 / 2013
Studia Mathematica 215 (2013), 281-285
MSC: 46E30, 46B45, 46B15.
DOI: 10.4064/sm215-3-5
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)}=\left\|\sum_k \|\sum_l a_{k,l}f_l\|e_k\right\| $ embeds into $L_1$. This generalizes a recent result of Prochno and Schütt.
