Norm continuity of weakly quasi-continuous mappings
Volume 122 / 2011
Colloquium Mathematicum 122 (2011), 83-91
MSC: Primary 54C08, 54E52, 46B20; Secondary 46B45, 54C35.
DOI: 10.4064/cm122-1-8
Abstract
Let $\mathcal{Q}$ be the class of Banach spaces $X$ for which every weakly quasi-continuous mapping $f: A \rightarrow X$ defined on an $\alpha$-favorable space $A$ is norm continuous at the points of a dense $G_\delta$ subset of $A$. We will show that this class is stable under $c_0$-sums and $\ell^p$-sums of Banach spaces for $1 \leq p < \infty$.
