线性算子幂乘积的正交可加性

IF 0.6 4区数学 Q3 MATHEMATICS

Mathematical Notes Pub Date : 2024-03-12 DOI:10.1134/s0001434623110615

Z. A. Kusraeva, V. A. Tamaeva

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引用次数: 0

摘要

摘要本论文证明了从阿基米德向量晶格作用到具有单位的阿基米德（f\）代数中的正线性算子的有限族是不相交的，当且仅当以这些算子的幂的乘积形式呈现的多项式是正交可加的。对于以正算子幂积形式表示的多项式之和，也有类似的说法。

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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Orthogonal Additivity of a Product of Powers of Linear Operators

Abstract

In this note it is established that a finite family of positive linear operators acting from an Archimedean vector lattice into an Archimedean \(f\)-algebra with unit is disjointness preserving if and only if the polynomial presented in the form of the product of powers of these operators is orthogonally additive. A similar statement is established for the sum of polynomials represented as products of powers of positive operators.

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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.