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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.
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 -