On operators from separable reflexive spaces with asymptotic structure

Bentuo Zheng. "On operators from separable reflexive spaces with asymptotic structure." Studia Mathematica 185.1 (2008): 87-98. <http://eudml.org/doc/286583>.

@article{BentuoZheng2008,
abstract = {Let 1 < q < p < ∞ and q ≤ r ≤ p. Let X be a reflexive Banach space satisfying a lower-$ℓ_\{q\}$-tree estimate and let T be a bounded linear operator from X which satisfies an upper-$ℓ_\{p\}$-tree estimate. Then T factors through a subspace of $(∑ Fₙ)_\{ℓ_\{r\}\}$, where (Fₙ) is a sequence of finite-dimensional spaces. In particular, T factors through a subspace of a reflexive space with an $(ℓ_\{p\}, ℓ_\{q\})$ FDD. Similarly, let 1 < q < r < p < ∞ and let X be a separable reflexive Banach space satisfying an asymptotic lower-$ℓ_\{q\}$-tree estimate. Let T be a bounded linear operator from X which satisfies an asymptotic upper-$ℓ_\{p\}$-tree estimate. Then T factors through a subspace of $(∑ Gₙ)_\{ℓ_\{r\}\}$, where (Gₙ) is a sequence of finite-dimensional spaces. In particular, T factors through a subspace of a reflexive space with an asymptotic $(ℓ_\{p\},ℓ_\{q\})$ FDD.},
author = {Bentuo Zheng},
journal = {Studia Mathematica},
keywords = {lower--tree estimate; upper--tree estimate; asymptotic lower--tree estimate; asymptotic upper--tree estimate; factorizations},
language = {eng},
number = {1},
pages = {87-98},
title = {On operators from separable reflexive spaces with asymptotic structure},
url = {http://eudml.org/doc/286583},
volume = {185},
year = {2008},
}

TY - JOUR
AU - Bentuo Zheng
TI - On operators from separable reflexive spaces with asymptotic structure
JO - Studia Mathematica
PY - 2008
VL - 185
IS - 1
SP - 87
EP - 98
AB - Let 1 < q < p < ∞ and q ≤ r ≤ p. Let X be a reflexive Banach space satisfying a lower-$ℓ_{q}$-tree estimate and let T be a bounded linear operator from X which satisfies an upper-$ℓ_{p}$-tree estimate. Then T factors through a subspace of $(∑ Fₙ)_{ℓ_{r}}$, where (Fₙ) is a sequence of finite-dimensional spaces. In particular, T factors through a subspace of a reflexive space with an $(ℓ_{p}, ℓ_{q})$ FDD. Similarly, let 1 < q < r < p < ∞ and let X be a separable reflexive Banach space satisfying an asymptotic lower-$ℓ_{q}$-tree estimate. Let T be a bounded linear operator from X which satisfies an asymptotic upper-$ℓ_{p}$-tree estimate. Then T factors through a subspace of $(∑ Gₙ)_{ℓ_{r}}$, where (Gₙ) is a sequence of finite-dimensional spaces. In particular, T factors through a subspace of a reflexive space with an asymptotic $(ℓ_{p},ℓ_{q})$ FDD.
LA - eng
KW - lower--tree estimate; upper--tree estimate; asymptotic lower--tree estimate; asymptotic upper--tree estimate; factorizations
UR - http://eudml.org/doc/286583
ER -