Compactness in the space of $p$-continuous vector-valued functions
Volume 249 / 2019
Studia Mathematica 249 (2019), 303-318
MSC: Primary 46B50; Secondary 46B20, 46B25, 46E15.
DOI: 10.4064/sm180203-12-11
Published online: 28 June 2019
Abstract
Let $X$ be a Banach space and let $\Omega $ be a compact Hausdorff space. We prove a characterization of compact sets in the spaces $\mathcal {C}_{p}(\Omega ,X)$ of $p$-continuous functions on $\Omega $, $1\leq p\leq \infty $, with $\mathcal {C}(\Omega ,X)=\mathcal {C}_{\infty }(\Omega ,X)$. We also establish a necessary condition and a sufficient condition for a set in $\mathcal {C}_{p}(\Omega ,X)$ to be $p$-compact.
