Description

• Title:
  Compactness in spaces of p-integrable functions with respect to a vector measure
• Creator:
  Rueda, Pilar;
  Sánchez-Pérez, Enrique A.
• Description:
  We prove that, under some reasonable requirements, the unit balls of the spaces $L^p(m)$ and $L^\infty(m)$ of a vector measure of compact range $m$ are compact with respect to the topology $\tau_m$ of pointwise convergence of the integrals. This result can be considered as a generalization of the classical Alaoglu Theorem to spaces of $p$-integrable functions with respect to vector measures with relatively compact range. Some applications to the analysis of the Saks spaces defined by the norm topology and $\tau_m$ are given.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2015 Topological Methods in Nonlinear Analysis
• Date:
  2015.06.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 45, No 2 (June 2015); 641 - 653;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2015.030/7462
• Subject:
  Banach function space;
  vector measure integration;
  compactness;
  46A50;
  46B50;
  46E30;
  46G10
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2015.030
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other