A+ CATEGORY SCIENTIFIC UNIT

Matrix subspaces of $L_1$

Volume 215 / 2013

Gideon Schechtman 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.

Authors

  • Gideon SchechtmanDepartment of Mathematics
    Weizmann Institute of Science
    Rehovot, Israel
    e-mail

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