凸性条件下的自由Banach格。

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2022-01-01 Epub Date: 2021-10-11 DOI:10.1007/s13398-021-01155-8

Héctor Jardón-Sánchez, Niels Jakob Laustsen, Mitchell A Taylor, Pedro Tradacete, Vladimir G Troitsky

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引用次数: 10

摘要

我们证明了Banach格的某些子范畴中自由对象的存在性，包括p-凸Banach格、具有上p估计的Banach格和am空间。由此，我们立即推断出这些子类别中存在投影普遍对象，扩展了Leung, Li, Oikhberg和Tursi (Israel J. Math. 2019)的结果。在p-凸和am空间的情况下，我们能够明确地识别自由Banach格的范数，并通过研究这些范数与非线性p-和映射的关系得出结论。

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Free Banach lattices under convexity conditions.

We prove the existence of free objects in certain subcategories of Banach lattices, including p-convex Banach lattices, Banach lattices with upper p-estimates, and AM-spaces. From this we immediately deduce that projectively universal objects exist in each of these subcategories, extending results of Leung, Li, Oikhberg and Tursi (Israel J. Math. 2019). In the p-convex and AM-space cases, we are able to explicitly identify the norms of the free Banach lattices, and we conclude by investigating the structure of these norms in connection with nonlinear p-summing maps.

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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.

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