On vector measures with values in c₀(κ)

2024/04/08 by José Rodríguez, Rodríguez, José · 1 citation
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2404.05407

openalex publication_date 2024/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

Let ν be a vector measure defined on a σ-algebra Σ and taking values in a Banach space. We prove that if ν is homogeneous and L₁(ν) is non-separable, then there is a vector measure ν:Σ→ c₀(κ) such that L₁(ν)=L₁(ν) with equal norms, where κ is the density character of L₁(ν). This is a non-separable version of a result of [G.P. Curbera, Pacific J. Math. 162 (1994), no. 2, 287--303].

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