Okada, S.; Ricker, W. J. Criteria for weak compactness of vector-valued integration maps. (English) Zbl 0805.46040 Commentat. Math. Univ. Carol. 35, No. 3, 485-495 (1994). Summary: Criteria are given for determining the weak compactness, or otherwise, of the integration map associated with a vector measure. For instance, the space of integrable functions of a weakly compact integration map is necessarily normable for the mean convergence topology. Results are presented which relate weak compactness of the integration map with the property of being a bicontinuous isomorphism onto its range. Finally, a detailed description is given of the compactness properties for the integration maps of a class of measures taking their values in \(\ell^ 1\), equipped with various weak topologies. Cited in 2 Documents MSC: 46G10 Vector-valued measures and integration 46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 47B07 Linear operators defined by compactness properties 46A03 General theory of locally convex spaces Keywords:weakly compact integration map; factorization of a vector measure; weak compactness; integration map associated with a vector measure; space of integrable functions of a weakly compact integration map; mean convergence topology; bicontinuous isomorphism PDFBibTeX XMLCite \textit{S. Okada} and \textit{W. J. Ricker}, Commentat. Math. Univ. Carol. 35, No. 3, 485--495 (1994; Zbl 0805.46040) Full Text: EuDML