Extension and lifting of weakly continuous polynomials

Raffaella Cilia, and Joaquín M. Gutiérrez. "Extension and lifting of weakly continuous polynomials." Studia Mathematica 169.3 (2005): 229-241. <http://eudml.org/doc/284427>.

@article{RaffaellaCilia2005,
abstract = {We show that a Banach space X is an ℒ₁-space (respectively, an $ℒ_\{∞\}$-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 $_\{wb\}(^\{m\}X)$ of m-homogeneous scalar-valued polynomials on X which are weakly continuous on bounded sets is an $ℒ_\{∞\}$-space.},
author = {Raffaella Cilia, Joaquín M. Gutiérrez},
journal = {Studia Mathematica},
keywords = {weakly continuous polynomial; extension; lifting; -space; -space},
language = {eng},
number = {3},
pages = {229-241},
title = {Extension and lifting of weakly continuous polynomials},
url = {http://eudml.org/doc/284427},
volume = {169},
year = {2005},
}

TY - JOUR
AU - Raffaella Cilia
AU - Joaquín M. Gutiérrez
TI - Extension and lifting of weakly continuous polynomials
JO - Studia Mathematica
PY - 2005
VL - 169
IS - 3
SP - 229
EP - 241
AB - We show that a Banach space X is an ℒ₁-space (respectively, an $ℒ_{∞}$-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 $_{wb}(^{m}X)$ of m-homogeneous scalar-valued polynomials on X which are weakly continuous on bounded sets is an $ℒ_{∞}$-space.
LA - eng
KW - weakly continuous polynomial; extension; lifting; -space; -space
UR - http://eudml.org/doc/284427
ER -