{"title":"On Disjointness-Preserving Biadditive Operators","authors":"N. A. Dzhusoeva","doi":"10.1134/s0001434624050079","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> Orthogonally biadditive operators preserving disjointness are studied. It is proved that, that for a Dedekind complete vector lattice <span>\\(W\\)</span> and order ideals <span>\\(E\\)</span> and <span>\\(F\\)</span> in <span>\\(W\\)</span>, the set <span>\\(\\mathfrak{N}(E,F;W)\\)</span> of all orthogonally biadditive operators commuting with projections is a band in the Dedekind complete vector lattice <span>\\(\\mathcal{OBA}_r(E,F;W)\\)</span> of all regular orthogonally biadditive operators from the Cartesian product of <span>\\(E\\)</span> and <span>\\(F\\)</span> to <span>\\(W\\)</span>. A general form of the order projection onto this band is obtained, and an operator version of the Radon–Nikodym theorem for disjointness-preserving positive orthogonally biadditive operators is proved. </p>","PeriodicalId":18294,"journal":{"name":"Mathematical Notes","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Notes","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0001434624050079","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Orthogonally biadditive operators preserving disjointness are studied. It is proved that, that for a Dedekind complete vector lattice \(W\) and order ideals \(E\) and \(F\) in \(W\), the set \(\mathfrak{N}(E,F;W)\) of all orthogonally biadditive operators commuting with projections is a band in the Dedekind complete vector lattice \(\mathcal{OBA}_r(E,F;W)\) of all regular orthogonally biadditive operators from the Cartesian product of \(E\) and \(F\) to \(W\). A general form of the order projection onto this band is obtained, and an operator version of the Radon–Nikodym theorem for disjointness-preserving positive orthogonally biadditive operators is proved.
期刊介绍：
Mathematical Notes is a journal that publishes research papers and review articles in modern algebra, geometry and number theory, functional analysis, logic, set and measure theory, topology, probability and stochastics, differential and noncommutative geometry, operator and group theory, asymptotic and approximation methods, mathematical finance, linear and nonlinear equations, ergodic and spectral theory, operator algebras, and other related theoretical fields. It also presents rigorous results in mathematical physics.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
