正交加性算子的片段与非线性dods - fremlin定理

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications Pub Date : 2025-04-02 DOI:10.1016/j.jmaa.2025.129551

Karimbergen Kudaybergenov , Marat Pliev , Fedor Sukochev

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引用次数: 0

摘要

本文第一部分描述了正正交可加算子T:E→F的所有片段的布尔代数FT的结构，将Aliprantis， Burkinshaw， de Pagter的经典结果推广到Banach格上正交可加（一般非线性）算子的集合。在文章的第二部分，我们给出了著名的多兹-弗雷姆林定理的非线性版本。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Fragments of orthogonally additive operators and the nonlinear Dodds-Fremlin's theorem

In the first part of the paper we describe the structure of the Boolean algebra

F_{T}

of all fragments of a positive orthogonally additive operator

T : E \to F

, generalizing classical results of Aliprantis, Burkinshaw, de Pagter to the setting of orthogonally additive (in general nonlinear) operators on Banach lattices. In the second part of the article we present the nonlinear version of the well known Dodds-Fremlin's theorem.

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来源期刊

Journal of Mathematical Analysis and Applications 数学-数学

CiteScore

2.50

自引率

7.70%

发文量

790

审稿时长

6 months

期刊介绍： The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions. Papers are sought which employ one or more of the following areas of classical analysis: • Analytic number theory • Functional analysis and operator theory • Real and harmonic analysis • Complex analysis • Numerical analysis • Applied mathematics • Partial differential equations • Dynamical systems • Control and Optimization • Probability • Mathematical biology • Combinatorics • Mathematical physics.