We show that a Banach space $X$ is an ${\mathscr L}_1$-space (respectively, an ${\mathscr L}_\infty$-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 ${\mathscr L}_1$-space if and only if the space $\pwbmX$ of $m$-homogeneous scalar-valued polynomials on $X$ which are weakly continuous on bounded sets is an ${\mathscr L}_\infty$-space.
Extension and lifting of weakly Continuous Polynomials
CILIA, Raffaela Giovanna;
2005-01-01
Abstract
We show that a Banach space $X$ is an ${\mathscr L}_1$-space (respectively, an ${\mathscr L}_\infty$-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 ${\mathscr L}_1$-space if and only if the space $\pwbmX$ of $m$-homogeneous scalar-valued polynomials on $X$ which are weakly continuous on bounded sets is an ${\mathscr L}_\infty$-space.File in questo prodotto:
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