We study compactness and related topological properties in the space L¹(m) of a Banach space valued measure m when the natural topologies associated to convergence of vector valued integrals are considered. The resulting topological spaces are shown to be angelic and the relationship of compactness and equi-integrability is explored. A natural norming subset of the dual unit ball of L¹(m) appears in our discussion and we study when it is a boundary. The (almost) complete continuity of the integration operator is analyzed in relation with the positive Schur property of L¹(m). The strong weakly compact generation of L¹(m) is discussed as well.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm225-3-6,
author = {J. M. Calabuig and S. Lajara and J. Rodr\'\i guez and E. A. S\'anchez-P\'erez},
title = {Compactness in L$^1$ of a vector measure},
journal = {Studia Mathematica},
volume = {223},
year = {2014},
pages = {259-282},
zbl = {1332.46037},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm225-3-6}
}
J. M. Calabuig; S. Lajara; J. Rodríguez; E. A. Sánchez-Pérez. Compactness in L¹ of a vector measure. Studia Mathematica, Tome 223 (2014) pp. 259-282. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm225-3-6/