论保留不相关性的双加法算子

IF 0.6 4区数学 Q3 MATHEMATICS Mathematical Notes Pub Date : 2024-07-15 DOI:10.1134/s0001434624050079

N. A. Dzhusoeva

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引用次数: 0

摘要

摘要研究了保持不相交性的正交双加法算子。研究证明，对于一个 Dedekind 完全向量网格（W）和在（W）中的阶理想（E）和（F），所有与投影相交的正交双相加算子的集合（mathfrak{N}(E,F.W)）是 Dedekind 中的一个带；W)）中所有与投影相通的正交双向算子的集合是从\(E\)和\(F\)的笛卡尔积到\(W\)的所有正交双向算子的戴德金完全向量网格\(\mathcal{OBA}_r(E,F;W)\)中的一个带。得到了这个带的阶投影的一般形式，并证明了不相交保留正交双相加算子的 Radon-Nikodym 定理的算子版本。

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On Disjointness-Preserving Biadditive Operators

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.

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来源期刊

Mathematical Notes 数学-数学

CiteScore

0.90

自引率

16.70%

发文量

179

审稿时长

24 months

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.