Criteria for weak compactness of vector-valued integration maps
Okada, Susumu ; Ricker, Werner J.
Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994), p. 485-495 / Harvested from Czech Digital Mathematics Library
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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.

Publié le : 1994-01-01
Classification:  28B05,  46A05,  46E30,  46G10,  47B07,  47B38 
@article{118688,
     author = {Susumu Okada and Werner J. Ricker},
     title = {Criteria for weak compactness of vector-valued integration maps},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {35},
     year = {1994},
     pages = {485-495},
     zbl = {0805.46040},
     mrnumber = {1307275},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118688}
}

Okada, Susumu; Ricker, Werner J. Criteria for weak compactness of vector-valued integration maps. Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994) pp. 485-495. http://gdmltest.u-ga.fr/item/118688/

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