2-summing multiplication operators

Dumitru Popa

Dumitru Popa

Studia Mathematica, Tome 215 (2013), p. 77-96 / Harvested from The Polish Digital Mathematics Library

Résumé

Let 1 ≤ p < ∞, $= {(X ₙ)}_{n \in ℕ}$ be a sequence of Banach spaces and $l_{p} ()$ the coresponding vector valued sequence space. Let $= {(X ₙ)}_{n \in ℕ}$ , $= {(Y ₙ)}_{n \in ℕ}$ be two sequences of Banach spaces, $= {(V ₙ)}_{n \in ℕ}$ , Vₙ: Xₙ → Yₙ, a sequence of bounded linear operators and 1 ≤ p,q < ∞. We define the multiplication operator $M_{} : l_{p} () \to l_{q} ()$ by $M_{} ({(x ₙ)}_{n \in ℕ}) : = {(V ₙ (x ₙ))}_{n \in ℕ}$ . We give necessary and sufficient conditions for $M_{}$ to be 2-summing when (p,q) is one of the couples (1,2), (2,1), (2,2), (1,1), (p,1), (p,2), (2,p), (1,p), (p,q); in the last case 1 < p < 2, 1 < q < ∞.

Publié le : 2013-01-01

Zbl 1288.47022

EUDML-ID : urn:eudml:doc:285383

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     title = {2-summing multiplication operators},
     journal = {Studia Mathematica},
     volume = {215},
     year = {2013},
     pages = {77-96},
     zbl = {1288.47022},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm216-1-6}
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Dumitru Popa. 2-summing multiplication operators. Studia Mathematica, Tome 215 (2013) pp. 77-96. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm216-1-6/