Matrix subspaces of L₁

Gideon Schechtman

Studia Mathematica, Tome 215 (2013), p. 281-285 / Harvested from The Polish Digital Mathematics Library

Résumé

If $E = e_{i}$ and $F = f_{i}$ are two 1-unconditional basic sequences in L₁ with E r-concave and F p-convex, for some 1 ≤ r < p ≤ 2, then the space of matrices $a_{i, j}$ with norm $| | a_{i, j} {| |}_{E (F)} = | | \sum_{k} | | \sum_{l} a_{k, l} f_{l} | | e_{k} | |$ embeds into L₁. This generalizes a recent result of Prochno and Schütt.

Publié le : 2013-01-01

Zbl 1287.46025

EUDML-ID : urn:eudml:doc:285801

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     title = {Matrix subspaces of L1},
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Gideon Schechtman. Matrix subspaces of L₁. Studia Mathematica, Tome 215 (2013) pp. 281-285. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm215-3-5/