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arXiv · 2502.21103

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

Geraldo Botelho·Luis Alberto Garcia·Vinícius C. C. Miranda
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Abstract

Let $E_1, \ldots, E_m$ be (non necessarily Archimedean) Riesz spaces, let $F$ be an Archimedean Riesz space and let $A \colon E_1 \times \cdots \times E_m \to F$ 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.

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Geraldo Botelho, Luis Alberto Garcia, Vinícius C. C. Miranda. 2025-02-28. Arens extensions of disjointness preserving multilinear operators on Riesz spaces and Banach lattices. https://arxiv.org/abs/2502.21103

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