Extension and lifting of weakly continuous polynomials
Volume 169 / 2005
Studia Mathematica 169 (2005), 229-241
MSC: Primary 46G25; Secondary 46B20, 47H60.
DOI: 10.4064/sm169-3-2
Abstract
We show that a Banach space $X$ is an ${\scr L}_1$-space (respectively, an ${\scr L}_\infty$-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 ${\scr L}_1$-space if and only if the space ${\cal P}_{{\rm wb}}(^m\!X)$ of $m$-homogeneous scalar-valued polynomials on $X$ which are weakly continuous on bounded sets is an ${\scr L}_\infty$-space.
