We show that a Banach space X is an ℒ₁-space (respectively, an -space) if and only if it has the lifting (respectively, the extension) property for polynomials which are weakly continuous on bounded sets. We also prove that X is an ℒ₁-space if and only if the space of m-homogeneous scalar-valued polynomials on X which are weakly continuous on bounded sets is an -space.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm169-3-2,
author = {Raffaella Cilia and Joaqu\'\i n M. Guti\'errez},
title = {Extension and lifting of weakly continuous polynomials},
journal = {Studia Mathematica},
volume = {166},
year = {2005},
pages = {229-241},
zbl = {1092.46031},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm169-3-2}
}
Raffaella Cilia; Joaquín M. Gutiérrez. Extension and lifting of weakly continuous polynomials. Studia Mathematica, Tome 166 (2005) pp. 229-241. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm169-3-2/