Multiple summing operators on $l_{p}$ spaces

Dumitru Popa

Multiple summing operators on

l_{p}

spaces

Dumitru Popa

Studia Mathematica, Tome 223 (2014), p. 9-28 / Harvested from The Polish Digital Mathematics Library

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Résumé

We use the Maurey-Rosenthal factorization theorem to obtain a new characterization of multiple 2-summing operators on a product of $l_{p}$ spaces. This characterization is used to show that multiple s-summing operators on a product of $l_{p}$ spaces with values in a Hilbert space are characterized by the boundedness of a natural multilinear functional (1 ≤ s ≤ 2). We use these results to show that there exist many natural multiple s-summing operators $T : l_{4 / 3} \times l_{4 / 3} \to l ₂$ such that none of the associated linear operators is s-summing (1 ≤ s ≤ 2). Further we show that if n ≥ 2, there exist natural bounded multilinear operators $T : l_{2 n / (n + 1)} \times \dots \times l_{2 n / (n + 1)} \to l ₂$ for which none of the associated multilinear operators is multiple s-summing (1 ≤ s ≤ 2).

Publié le : 2014-01-01

Zbl 1320.47060

EUDML-ID : urn:eudml:doc:285765

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     title = {Multiple summing operators on $l\_{p}$ spaces},
     journal = {Studia Mathematica},
     volume = {223},
     year = {2014},
     pages = {9-28},
     zbl = {1320.47060},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm225-1-2}
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Dumitru Popa. Multiple summing operators on $l_{p}$ spaces. Studia Mathematica, Tome 223 (2014) pp. 9-28. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm225-1-2/