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Gutman A.E.
Monotone operators in vector lattices and lattice-normed spaces //
Sib. Math. J. 2025. V. 66, N 3. P. 826–831.

We show that every monotone linear operator from a vector lattice to a lattice-normed space can 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.

Keywords:Riesz space, Banach lattice, lattice homomorphism, positive isometry, order isomorphism, lattice-normed space, Banach--Kantorovich space, Banach bundle, measurable section, lifting.
Type Article
Authors Gutman Alexander Efimovich
Title Monotone operators in vector lattices and lattice-normed spaces
Journal Siberian Mathematical Journal
Year 2025
Volume 66
Number 3
Pages 826–831
DOI 10.1134/S0037446625030188
Language English
© 2025.03.24
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Project  Bundles of Banach lattices 
Development of the theory of continuous and measurable bundles of Banach lattices and the theory of Banach–Kantorovich lattices
 
 
The papers are presented here for academic purposes and are not intended for mass dissemination or copying. Last updated
November 17, 2025