Dunford-Pettis type properties in L₁ of a vector measure

2024/04/08 by Rodríguez, José
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2404.05419

Abstract

Let ν be a countably additive vector measure defined on a σ-algebra and taking values in a Banach space. In this paper we deal with the following three properties for the Banach lattice L₁(ν) of all ν-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.

Related

• L¹-spaces of vector measures with vector density
• On vector measures with values in ℓ_∞
• Open problems in Banach spaces and measure theory
• σ-unbounded Dunford-Pettis operators on Banach lattices
• Reciprocal Dunford--Pettis sets and V^*-sets in Banach lattices