巴拿赫空间中的对偶锥和广义对偶锥

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-06-11 DOI:10.1007/s11590-024-02126-9

Akhtar A. Khan, Dezhou Kong, Jinlu Li

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引用次数: 0

摘要

本文提出并分析了与巴拿赫空间中的度量投影和广义投影相关的对偶锥概念。我们表明，与公投影和广义公投影相关的对偶锥在从希尔伯特空间过渡到巴拿赫空间时会失去许多重要性质。我们还提出并分析了巴拿赫空间中的面和视概念，并将它们与度量投影和广义投影联系起来。我们提供了许多说明性的例子，让大家深入了解所给出的结果

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Dual and generalized dual cones in Banach spaces

This paper proposes and analyzes the notion of dual cones associated with the metric projection and generalized projection in Banach spaces. We show that the dual cones, related to the metric projection and generalized metric projection, lose many important properties in transitioning from Hilbert spaces to Banach spaces. We also propose and analyze the notions of faces and visions in Banach spaces and relate them to metric projection and generalized projection. We provide many illustrative examples to give insight into the given results

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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.