On operators which factor through $l_p$ or c₀

Bentuo Zheng. "On operators which factor through $l_{p}$ or c₀." Studia Mathematica 176.2 (2006): 177-190. <http://eudml.org/doc/285025>.

@article{BentuoZheng2006,
abstract = {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 $(∑Fₙ)_\{l_\{p\}\}$, 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.},
author = {Bentuo Zheng},
journal = {Studia Mathematica},
keywords = {factorisation through ; finite-dimensional decomposition; weakly null trees},
language = {eng},
number = {2},
pages = {177-190},
title = {On operators which factor through $l_\{p\}$ or c₀},
url = {http://eudml.org/doc/285025},
volume = {176},
year = {2006},
}

TY - JOUR
AU - Bentuo Zheng
TI - On operators which factor through $l_{p}$ or c₀
JO - Studia Mathematica
PY - 2006
VL - 176
IS - 2
SP - 177
EP - 190
AB - 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 $(∑Fₙ)_{l_{p}}$, 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.
LA - eng
KW - factorisation through ; finite-dimensional decomposition; weakly null trees
UR - http://eudml.org/doc/285025
ER -