Compactness in $L^1$ of a vector measure
Studia Mathematica, Tome 225 (2014) no. 3, pp. 259-282
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
We study compactness and related topological properties in the space $L^1(m)$ 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 $L^1(m)$ 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 $L^1(m)$. The strong weakly compact generation of $L^1(m)$ is discussed as well.
Keywords:
study compactness related topological properties space banach space valued measure nbsp natural topologies associated convergence vector valued integrals considered resulting topological spaces shown angelic relationship compactness equi integrability explored natural norming subset dual unit ball nbsp appears discussion study boundary almost complete continuity integration operator analyzed relation positive schur property nbsp strong weakly compact generation nbsp discussed
Affiliations des auteurs :
J. M. Calabuig 1 ; S. Lajara 2 ; J. Rodríguez 3 ; E. A. Sánchez-Pérez 1
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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},
pages = {259--282},
publisher = {mathdoc},
volume = {225},
number = {3},
year = {2014},
doi = {10.4064/sm225-3-6},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm225-3-6/}
}
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J. M. Calabuig; S. Lajara; J. Rodríguez; E. A. Sánchez-Pérez. Compactness in $L^1$ of a vector measure. Studia Mathematica, Tome 225 (2014) no. 3, pp. 259-282. doi: 10.4064/sm225-3-6
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