## Illinois Journal of Mathematics

### Compactness arguments for spaces of $p$-integrable functions with respect to a vector measure and factorization of operators through Lebesgue-Bochner spaces

E. A. Sánchez Pérez

#### Abstract

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.

#### Article information

Source
Illinois J. Math., Volume 45, Number 3 (2001), 907-923.

Dates
First available in Project Euclid: 13 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258138159

Digital Object Identifier
doi:10.1215/ijm/1258138159

Mathematical Reviews number (MathSciNet)
MR1879243

Zentralblatt MATH identifier
0992.46035

#### Citation

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. 45 (2001), no. 3, 907--923. doi:10.1215/ijm/1258138159. https://projecteuclid.org/euclid.ijm/1258138159