2015/07/27 by Marat Pliev, Pliev, Marat A.
Mathematics · #47H30 #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.1507.07549
openalex publication_date 2015/07/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The "Up-and-down" theorem which describes the structure of the Boolean algebra of fragments of a linear positive operator is the well known result of the operator theory. We prove an analog of this theorem for a positive abstract Uryson operator defined on a vector lattice and taking values in a Dedekind complete vector lattice. This result we apply to prove that for an order narrow positive abstract Uryson operator T from a vector lattice E to a Dedekind complete vector lattice F, every abstract Uryson operator S:E→ F, such that 0≤ S≤ T is also order narrow.