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This is a Quantitative Study study.

October 3, 2025Open Access

Compact positive multilinear operators on Banach lattices

Key Points

Positive n-linear operators from ℓp to Lq are shown to be compact, contributing to the understanding of operator theory.
If the condition ∑(1/pi) < 1/q holds, we prove compactness for both types of positive multilinear operators.
The results extend known linear operator results, indicating further implications for free Banach lattices.
We establish facts about M-weakly compact multilinear operators, broadening the scope of understanding in functional analysis.

Abstract

Let 1 < p₁, , pₙ <, 1 q < be such that ₈=₁ⁿ 1pᵢ < 1q and let μ₁, , μₙ, ν be arbitrary measures. Generalizing known linear and multilinear results, we prove that all positive n-linear operators from ₏䃑 ₏䂸 to Lq (ν) and from L₏䃑 (μ₁) L₏䃑 (μₙ) to ₐ are compact. This result, along with other related ones concerning free Banach lattices, shall emerge as consequences of some facts we prove about M-weakly compact multilinear operators on Banach lattices.

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Botelho et al. (Thu,) studied this question.

synapsesocial.com/papers/68e02f46f0e39f13e7fa2ba9 https://doi.org/https://doi.org/10.48550/arxiv.2509.04652