Geodesic
Criteria for weak compactness of vector-valued integration maps
Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994) no. 3, pp. 485-495
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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.
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.
Classification : 28B05, 46A05, 46E30, 46G10, 47B07, 47B38
Keywords: weakly compact integration map; factorization of a vector measure 
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     author = {Okada, S. and Ricker, W. J.},
     title = {Criteria for weak compactness of vector-valued integration maps},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
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     year = {1994},
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}
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Okada, S.; Ricker, W. J. Criteria for weak compactness of vector-valued integration maps. Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994) no. 3, pp. 485-495. http://geodesic.mathdoc.fr/item/CMUC_1994_35_3_a5/