On operators which factor through $l_{p}$ or c₀
Studia Mathematica, Tome 176 (2006) no. 2, p. 177.

Voir la notice de l'article dans European Digital Mathematics Library

Let 1 < p < ∞. Let X be a subspace of a space Z with a shrinking F.D.D. (Eₙ) which satisfies a block lower-p estimate. Then any bounded linear operator T from X which satisfies an upper-(C,p)-tree estimate factors through a subspace of ( ∑ F ₙ ) l p , where (Fₙ) is a blocking of (Eₙ). In particular, we prove that an operator from L p (2 < p < ∞) satisfies an upper-(C,p)-tree estimate if and only if it factors through l p . This gives an answer to a question of W. B. Johnson. We also prove that if X is a Banach space with X* separable and T is an operator from X which satisfies an upper-(C,∞)-estimate, then T factors through a subspace of c₀.
Classification : 46B03, 46B25
Mots-clés : factorisation through, finite-dimensional decomposition, weakly null trees 
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Bentuo Zheng. On operators which factor through $l_{p}$ or c₀. Studia Mathematica, Tome 176 (2006) no. 2, p. 177. https://geodesic-test.mathdoc.fr/item/STUMA_2006__176_2_285025/