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

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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

Subjects
Primary: 46G10: Vector-valued measures and integration [See also 28Bxx, 46B22]
Secondary: 28B05: Vector-valued set functions, measures and integrals [See also 46G10] 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 46E40: Spaces of vector- and operator-valued functions

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


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