Diffuse orthogonally additive operators

Nariman Magamedovich Abasov; Nonna Anatolevna Dzhusoeva; Marat Amurkhanovich Pliev

doi:10.4213/sm9909e

journal article Jan 01, 2024

Diffuse orthogonally additive operators

Nariman Magamedovich Abasov Nonna Anatolevna Dzhusoeva Marat Amurkhanovich Pliev

Sbornik: Mathematics Vol. 215 No. 1 pp. 1-27 · Steklov Mathematical Institute

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Abstract

A regular orthogonally additive operator is a diffuse operator if it is disjoint from all operators in the band generated by the disjointness preserving operators. We present a criterion for principal lateral projections in an order complete vector lattice $E$ to be disjoint. We also state a criterion for a regular orthogonally additive operator to be diffuse. A criterion for the regularity of an integral Urysohn operator acting on ideal spaces of measurable functions is also presented. This criterion is used to show that an integral operator is diffuse. Examples of vector lattices are considered in which the sets of diffuse operators consist only of the zero element. The general form of an order projection operator onto the band generated by the disjointness preserving operators is found.
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Details

Published: Jan 01, 2024
Vol/Issue: 215(1)
Pages: 1-27

Authors

N

Nariman Magamedovich Abasov

Bauman Moscow State Technical University, Moscow, Russia

N

Nonna Anatolevna Dzhusoeva

North Ossetian State University after Kosta Levanovich Khetagurov, Vladikavkaz, Russia

M

Marat Amurkhanovich Pliev

Southern Mathematical Institute of the Vladikavkaz Scientific Center of the Russian Academy of Sciences, Vladikavkaz, Russia; North Caucasus Center for Mathematical Research, Vladikavkaz Scientific Centre of the Russian Academy of Sciences, Vladikavkaz, Russia

Funding

Ministry of Science and Higher Education of the Russian Federation Award: 075-02-2023-914

Cite This Article

Nariman Magamedovich Abasov, Nonna Anatolevna Dzhusoeva, Marat Amurkhanovich Pliev (2024). Diffuse orthogonally additive operators. Sbornik: Mathematics, 215(1), 1-27. https://doi.org/10.4213/sm9909e

Diffuse orthogonally additive operators

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