Arens extensions of disjointness preserving multilinear operators on Riesz spaces and Banach lattices

2025/02/28 by Botelho, Geraldo, Garcia, Luis Alberto, Miranda, Vinícius C. C.
#46A40 #46B24 #46G25 #47H60 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2502.21103

Abstract

Let E₁, …, E_m be (non necessarily Archimedean) Riesz spaces, let F be an Archimedean Riesz space and let A \colon E₁ × ⋯ × E_m → F be a regular disjointness preserving m-linear operator. We prove that all Arens extensions of A are disjointness preserving if either A has finite lattice rank or the spaces are Banach lattices and F^* has a Schauder basis consisting of disjointness preserving functionals.

Related

• Unbounded Disjointness Preserving Linear Functionals and Operators
• Bidual extensions of Riesz multimorphisms
• Operators Affiliated to Banach Lattice Properties and the Enveloping Norms
• Disjointly homogeneous Banach lattices and applications
• Riesz completions of some spaces of regular operators