Geodesic
On Completely Continuous Integration Operators of a Vector Measure
Journal of convex analysis, Tome 21 (2014) no. 3, pp. 811-818.

Voir la notice de l'article provenant de la source Heldermann Verlag

Let $m$ be a vector measure taking values in a Banach space $X$. We prove that if the integration operator $I_m: L^1(m) \to X$, $I_m(f)=\int f \, dm$, is completely continuous and $X$ is Asplund, then $m$ has finite variation and $L^1(m) =L^1(|m|)$.
Classification : 46E30, 46G10, 47B07
Mots-clés : Integration operator, vector measure, completely continuous operator, Asplund space 
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     author = {J. M. Calabuig and J. Rodr{\'\i}guez and E. A. S\'anchez-P\'erez},
     title = {On {Completely} {Continuous} {Integration} {Operators} of a {Vector} {Measure}},
     journal = {Journal of convex analysis},
     pages = {811--818},
     publisher = {mathdoc},
     volume = {21},
     number = {3},
     year = {2014},
     url = {http://geodesic.mathdoc.fr/item/JCA_2014_21_3_JCA_2014_21_3_a11/}
}
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J. M. Calabuig; J. Rodríguez; E. A. Sánchez-Pérez. On Completely Continuous Integration Operators of a Vector Measure. Journal of convex analysis, Tome 21 (2014) no. 3, pp. 811-818. http://geodesic.mathdoc.fr/item/JCA_2014_21_3_JCA_2014_21_3_a11/