The Maurey extension property for Banach spaces with the Gordon-Lewis property and related structures

P. G. Casazza, and N. J. Nielsen. "The Maurey extension property for Banach spaces with the Gordon-Lewis property and related structures." Studia Mathematica 155.1 (2003): 1-21. <http://eudml.org/doc/285038>.

@article{P2003,
abstract = {The main result of this paper states that if a Banach space X has the property that every bounded operator from an arbitrary subspace of X into an arbitrary Banach space of cotype 2 extends to a bounded operator on X, then every operator from X to an L₁-space factors through a Hilbert space, or equivalently $B(ℓ_\{∞\},X*) = Π₂(ℓ_\{∞\},X*)$. If in addition X has the Gaussian average property, then it is of type 2. This implies that the same conclusion holds if X has the Gordon-Lewis property (in particular X could be a Banach lattice) or if X is isomorphic to a subspace of a Banach lattice of finite cotype, thus solving the Maurey extension problem for these classes of spaces. The paper also contains a detailed study of the property of extending operators with values in $ℓ_\{p\}$-spaces, 1 ≤ p < ∞.},
author = {P. G. Casazza, N. J. Nielsen},
journal = {Studia Mathematica},
keywords = {factorisation through Hilbert space; type; cotype; Maurey extension property; Gordon-Lewis proeprty; Gaussian average property},
language = {eng},
number = {1},
pages = {1-21},
title = {The Maurey extension property for Banach spaces with the Gordon-Lewis property and related structures},
url = {http://eudml.org/doc/285038},
volume = {155},
year = {2003},
}

TY - JOUR
AU - P. G. Casazza
AU - N. J. Nielsen
TI - The Maurey extension property for Banach spaces with the Gordon-Lewis property and related structures
JO - Studia Mathematica
PY - 2003
VL - 155
IS - 1
SP - 1
EP - 21
AB - The main result of this paper states that if a Banach space X has the property that every bounded operator from an arbitrary subspace of X into an arbitrary Banach space of cotype 2 extends to a bounded operator on X, then every operator from X to an L₁-space factors through a Hilbert space, or equivalently $B(ℓ_{∞},X*) = Π₂(ℓ_{∞},X*)$. If in addition X has the Gaussian average property, then it is of type 2. This implies that the same conclusion holds if X has the Gordon-Lewis property (in particular X could be a Banach lattice) or if X is isomorphic to a subspace of a Banach lattice of finite cotype, thus solving the Maurey extension problem for these classes of spaces. The paper also contains a detailed study of the property of extending operators with values in $ℓ_{p}$-spaces, 1 ≤ p < ∞.
LA - eng
KW - factorisation through Hilbert space; type; cotype; Maurey extension property; Gordon-Lewis proeprty; Gaussian average property
UR - http://eudml.org/doc/285038
ER -