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Compactness in L¹ of a vector measure

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Calabuig J., Lajara S., Rodríguez J., Sánchez-Pérez E.

Studia Mathematica

2014

tom 225

nr 3

259-282

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.

Ograniczanie wyników

1 Studia Mathematica

1 Calabuig J.

1 Lajara S.

1 Rodríguez J.

1 Sánchez-Pérez E.

1 2014

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Compactness in L¹ of a vector measure