Isometries of absolutely continuous function spaces with respect to the sum-norm

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-03-26 DOI:10.1007/s13324-024-00894-2

Maliheh Hosseini, Juan J. Font

引用次数: 0

Abstract

In this paper we give a complete description of surjective linear isometries between Banach spaces of absolutely continuous functions on arbitrary (not necessarily compact) subsets of the real line with respect to the sum-norm. We also use this description to study approximate local isometries and approximate 2-local isometries on these spaces. In particular, we present generalizations of all known results concerning such isometries, and obtain the reflexivity and 2-reflexivity of the isometry group of absolutely continuous function spaces in a noncompact framework.

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绝对连续函数空间关于和规范的等距性

在本文中，我们完整地描述了实线的任意（不一定紧凑）子集上绝对连续函数的巴拿赫空间之间关于和规范的线性等距。我们还利用这一描述来研究这些空间上的近似局部等距和近似 2 局部等距。特别是，我们提出了有关此类等距的所有已知结果的一般化，并获得了绝对连续函数空间等距群在非紧凑框架中的反射性和 2 反射性。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.