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arXiv · 2404.05419

Dunford-Pettis type properties in $L_1$ of a vector measure

José Rodríguez
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Abstract

Let $\nu$ be a countably additive vector measure defined on a $\sigma$-algebra and taking values in a Banach space. In this paper we deal with the following three properties for the Banach lattice $L_1(\nu)$ of all $\nu$-integrable real-valued functions: the Dunford-Pettis property, the positive Schur property and being lattice-isomorphic to an AL-space. We give new results and we also provide alternative proofs of some already known ones.

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José Rodríguez. 2024-04-08. Dunford-Pettis type properties in $L_1$ of a vector measure. https://arxiv.org/abs/2404.05419

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