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 , where (Fₙ) is a blocking of (Eₙ). In particular, we prove that an operator from (2 < p < ∞) satisfies an upper-(C,p)-tree estimate if and only if it factors through . 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm176-2-5,
author = {Bentuo Zheng},
title = {On operators which factor through $l\_{p}$ or c0},
journal = {Studia Mathematica},
volume = {173},
year = {2006},
pages = {177-190},
zbl = {1117.46008},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm176-2-5}
}
Bentuo Zheng. On operators which factor through $l_{p}$ or c₀. Studia Mathematica, Tome 173 (2006) pp. 177-190. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm176-2-5/