On Density and Bishop–Phelps–Bollobás-Type Properties for the Minimum Norm

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-08-02 DOI:10.1007/s00009-024-02705-1

Domingo García, Manuel Maestre, Miguel Martín, Óscar Roldán

引用次数: 0

Abstract

We study the set \({\text {MA}}(X,Y)\) of operators between Banach spaces X and Y that attain their minimum norm, and the set \({\text {QMA}}(X,Y)\) of operators that quasi attain their minimum norm. We characterize the Radon–Nikodym property in terms of operators that attain their minimum norm and obtain some related results about the density of the sets \({\text {MA}}(X,Y)\) and \({\text {QMA}}(X,Y)\). We show that every infinite-dimensional Banach space X has an isomorphic space Y, such that not every operator from X to Y quasi attains its minimum norm. We introduce and study Bishop–Phelps–Bollobás type properties for the minimum norm, including the ones already considered in the literature, and we exhibit a wide variety of results and examples, as well as exploring the relations between them.

Abstract Image

查看原文本刊更多论文

论最小规范的密度和毕晓普-菲尔普斯-波洛巴类型属性

我们研究了巴拿赫空间 X 和 Y 之间达到最小规范的算子集 \({\text {MA}}(X,Y)\) 以及准达到最小规范的算子集 \({\text {QMA}}(X,Y)\) 。我们用达到最小规范的算子来描述拉顿-尼科德姆性质，并得到了关于集合 \({\text {MA}}(X,Y)\) 和 \({\text {QMA}}(X,Y)\) 的密度的一些相关结果。我们证明了每一个无限维巴拿赫空间 X 都有一个同构空间 Y，这样就不是每一个从 X 到 Y 的算子都准达到其最小规范。我们引入并研究了最小规范的 Bishop-Phelps-Bollobás 类型性质，包括文献中已经考虑过的性质，并展示了各种结果和例子，同时探讨了它们之间的关系。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

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.