Quasi-linear functionals on locally compact spaces

Q4 Mathematics
S. Butler
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引用次数: 6

Abstract

This paper has two goals: to present some new results that are necessary for further study and applications of quasi-linear functionals, and, by combining known and new results, to serve as a convenient single source for anyone interested in quasi-linear functionals on locally compact non-compact spaces or on compact spaces. We study signed and positive quasi-linear functionals paying close attention to singly generated subalgebras. The paper gives representation theorems for quasi-linear functionals on $C_c(X)$ and for bounded quasi-linear functionals on $C_0(X)$ on a locally compact space, and for quasi-linear functionals on $C(X)$ on a compact space. There is an order-preserving bijection between quasi-linear functionals and compact-finite topological measures, which is also "isometric" when topological measures are finite. Finally, we further study properties of quasi-linear functionals and give an explicit example of a quasi-linear functional.
局部紧空间上的拟线性泛函
本文有两个目的:一是提出一些对拟线性泛函的进一步研究和应用所必需的新结果,二是将已知结果与新结果结合起来,为那些对局部紧致非紧致空间或紧致空间上的拟线性泛函感兴趣的人提供一个方便的单一来源。我们研究了有符号和正拟线性泛函,重点关注单生成子代数。给出了$C_c(X)$上的拟线性泛函和$C_0(X)$上的有界拟线性泛函在局部紧化空间上的表示定理,以及$C(X)$上的拟线性泛函在紧化空间上的表示定理。拟线性泛函与紧有限拓扑测度之间存在保序双射,当拓扑测度是有限时,该双射也是“等距”的。最后,我们进一步研究了拟线性泛函的性质,并给出了一个拟线性泛函的显式例子。
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
Confluentes Mathematici
Confluentes Mathematici Mathematics-Mathematics (miscellaneous)
CiteScore
0.60
自引率
0.00%
发文量
5
期刊介绍: Confluentes Mathematici is a mathematical research journal. Since its creation in 2009 by the Institut Camille Jordan UMR 5208 and the Unité de Mathématiques Pures et Appliquées UMR 5669 of the Université de Lyon, it reflects the wish of the mathematical community of Lyon—Saint-Étienne to participate in the new forms of scientific edittion. The journal is electronic only, fully open acces and without author charges. The journal aims to publish high quality mathematical research articles in English, French or German. All domains of Mathematics (pure and applied) and Mathematical Physics will be considered, as well as the History of Mathematics. Confluentes Mathematici also publishes survey articles. Authors are asked to pay particular attention to the expository style of their article, in order to be understood by all the communities concerned.
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