Bidual extensions of Riesz multimorphisms

2021/08/09 by Geraldo Botelho, Botelho, Geraldo, Luis Alberto Garcia +1 · 1 citation
Mathematics · #Advanced Banach Space Theory #FOS: Mathematics #Functional Analysis (math.FA) #Functional Equations Stability Results #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2108.03769

openalex publication_date 2021/08/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that all Arens extensions of finite rank Riesz multimorphisms taking values in Archimedean Riesz spaces coincide and are Riesz multimorphisms. Partial results for arbitrary Riesz multimorphisms are obtained. We also prove that, for a class of Banach lattices F, which includes F = c₀, ℓ_p, c₀(ℓ_p), ℓ_p(c₀), ℓ_p(ℓ_s), 1 < p,s < ∞, among many others, all Aron-Berner extensions of F-valued Riesz multimorphisms between Banach lattices are Riesz multimorphisms.

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