Geodesic
Matrix subspaces of $L_1$
Gideon Schechtman1
1 Department of Mathematics Weizmann Institute of Science Rehovot, Israel
Studia Mathematica, Tome 215 (2013) no. 3, pp. 281-285 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm215-3-5
Keywords: unconditional basic sequences r concave p convex space matrices norm sum sum l right embeds generalizes recent result prochno sch

Gideon Schechtman 1

1 Department of Mathematics Weizmann Institute of Science Rehovot, Israel 
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Gideon Schechtman. Matrix subspaces of $L_1$. Studia Mathematica, Tome 215 (2013) no. 3, pp. 281-285. doi: 10.4064/sm215-3-5

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