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<p>We show that every monotone linear operator from a&#xa0;vector lattice to a&#xa0;lattice-normed spacecan be represented as the composition of a&#xa0;surjective lattice homomorphism and a&#xa0;linear isometry.We&#xa0;also give some applications to the theory of continuous and measurable bundles of Banach lattices.</p>

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Monotone Operators in Vector Lattices and Lattice-Normed Spaces

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年5月1日

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  • A. E. Gutman

摘要

We show that every monotone linear operator from a vector lattice to a lattice-normed spacecan be represented as the composition of a surjective lattice homomorphism and a linear isometry.We also give some applications to the theory of continuous and measurable bundles of Banach lattices.