Compactness arguments for spaces of $p$-integrable functions with respect to a vector measure and factorization of operators through Lebesgue-Bochner spaces
Sánchez Pérez, E. A.
Illinois J. Math., Tome 45 (2001) no. 4, p. 907-923 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
If $\lambda$ is a vector measure with values in a Banach space and $p > 1$, we consider the space of real functions $L_p(\lambda)$ that are $p$-integrable with respect to $\lambda$. We define two different vector valued dual topologies and we prove several compactness results for the unit ball of $L_p(\lambda)$. We apply these results to obtain new Grothendieck-Pietsch type factorization theorems.
Publié le : 2001-07-15
Classification:  46G10,  28B05,  46E30,  46E40 
@article{1258138159,
     author = {S\'anchez P\'erez, E. A.},
     title = {Compactness arguments for spaces of $p$-integrable functions with respect to a vector measure and factorization of operators through Lebesgue-Bochner spaces},
     journal = {Illinois J. Math.},
     volume = {45},
     number = {4},
     year = {2001},
     pages = { 907-923},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1258138159}
}

Sánchez Pérez, E. A. Compactness arguments for spaces of $p$-integrable functions with respect to a vector measure and factorization of operators through Lebesgue-Bochner spaces. Illinois J. Math., Tome 45 (2001) no. 4, pp.  907-923. http://gdmltest.u-ga.fr/item/1258138159/