无 Lipschitz p 空间的典型嵌入

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-04-15 DOI:10.1007/s43037-024-00339-9

Marek Cúth, Tomáš Raunig

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引用次数: 0

摘要

我们发现了一种新的有限算法，用于在有限维无 Lipschitz p 空间中评估无 Lipschitz p 空间规范。我们用这个算法来处理给定 p 空间 \(\mathcal {N}\subset \mathcal {M},\) 的 \(\mathcal {F}_p(\mathcal {N})\) 的规范嵌入到 \(\mathcal {F}_p(\mathcal {M})\) 是否是同构的问题。这个方向上最重要的结果是，如果 \(\mathcal {N}\subset \mathcal {M}\) 都是度量空间，答案就是肯定的。

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Canonical embedding of Lipschitz-free p-spaces

We find a new finite algorithm for evaluation of Lipschitz-free p-space norm in finite-dimensional Lipschitz-free p-spaces. We use this algorithm to deal with the problem of whether given p-metric spaces \(\mathcal {N}\subset \mathcal {M},\) the canonical embedding of \(\mathcal {F}_p(\mathcal {N})\) into \(\mathcal {F}_p(\mathcal {M})\) is an isomorphism. The most significant result in this direction is that the answer is positive if \(\mathcal {N}\subset \mathcal {M}\) are metric spaces.

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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.