Monotone Operators in Vector Lattices and Lattice-Normed Spaces
Abstract 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.
Authors
- А. Е. Гутман (ORCID: https://orcid.org/0000-0003-2030-7459)
Institutions
- Sobolev Institute of Mathematics (RU)
Publication Details
- Journal
- Siberian Mathematical Journal
- Published
- 2025-05-01
- DOI
- https://doi.org/10.1134/s0037446625030188
- Primary Topic
- Advanced Algebra and Logic
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences