Bulletin of the Belgian Mathematical Society - Simon Stevin

Representation of Banach lattices as $L_w^1$ spaces of a vector measure defined on a $\delta$-ring

O. Delgado and M. A. Juan

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Abstract

In this paper we prove that every Banach lattice having the Fatou property and having its $\sigma$-order continuous part as an order dense subset, can be represented as the space $L_w^1(\nu)$ of weakly integrable functions with respect to some vector measure $\nu$ defined on a $\delta$-ring.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 19, Number 2 (2012), 239-256.

Dates
First available in Project Euclid: 24 May 2012

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1337864270

Digital Object Identifier
doi:10.36045/bbms/1337864270

Mathematical Reviews number (MathSciNet)
MR2977229

Zentralblatt MATH identifier
1254.46045

Subjects
Primary: 46G10: Vector-valued measures and integration [See also 28Bxx, 46B22]
Secondary: 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 46B42: Banach lattices [See also 46A40, 46B40]

Keywords
Banach lattice $\delta$-ring Fatou property Order density Order continuity Integration with respect to vector measures

Citation

Delgado, O.; Juan, M. A. Representation of Banach lattices as $L_w^1$ spaces of a vector measure defined on a $\delta$-ring. Bull. Belg. Math. Soc. Simon Stevin 19 (2012), no. 2, 239--256. doi:10.36045/bbms/1337864270. https://projecteuclid.org/euclid.bbms/1337864270


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