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 . 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 -spaces, 1 ≤ p < ∞.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm155-1-1,
author = {P. G. Casazza and N. J. Nielsen},
title = {The Maurey extension property for Banach spaces with the Gordon-Lewis property and related structures},
journal = {Studia Mathematica},
volume = {157},
year = {2003},
pages = {1-21},
zbl = {1019.46008},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm155-1-1}
}
P. G. Casazza; N. J. Nielsen. The Maurey extension property for Banach spaces with the Gordon-Lewis property and related structures. Studia Mathematica, Tome 157 (2003) pp. 1-21. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm155-1-1/