Lack of Metric Projectivity, Injectivity, and Flatness for Modules \(L_p\)

IF 0.6 4区数学 Q3 MATHEMATICS

Functional Analysis and Its Applications Pub Date : 2025-01-20 DOI:10.1134/S0016266324040038

Norbert Nemesh

引用次数: 0

Abstract

In this paper, we demonstrate that for a locally compact Hausdorff space \(S\) and a decomposable Borel measure \(\mu\), metric projectivity, injectivity, or flatness of the \(C_0(S)\)-module \(L_p(S,\mu)\) implies that \(\mu\) is purely atomic with at most one atom.

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缺少度量投射性、注入性和模块平整度 \(L_p\)

在本文中，我们证明了对于一个局部紧化的Hausdorff空间\(S\)和一个可分解的Borel测度\(\mu\), \(C_0(S)\) -模\(L_p(S,\mu)\)的度量投影性、注入性或平面性意味着\(\mu\)是一个最多只有一个原子的纯原子。

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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来源期刊

Functional Analysis and Its Applications 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Functional Analysis and Its Applications publishes current problems of functional analysis, including representation theory, theory of abstract and functional spaces, theory of operators, spectral theory, theory of operator equations, and the theory of normed rings. The journal also covers the most important applications of functional analysis in mathematics, mechanics, and theoretical physics.