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Compactness in the space of $p$-continuous vector-valued functions

Volume 249 / 2019

Fernando Muñoz, Cándido Piñeiro 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.

Authors

  • Fernando MuñozDepartamento de Ciencias Experimentales
    Facultad de Ciencias Experimentales
    Universidad de Huelva
    Campus Universitario de El Carmen
    21071 Huelva, Spain
    e-mail
  • Cándido PiñeiroDepartamento de Ciencias Experimentales
    Facultad de Ciencias Experimentales
    Universidad de Huelva
    Campus Universitario de El Carmen
    21071 Huelva, Spain
    e-mail

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