凸性条件下的自由Banach格。

IF 1.8 2区数学 Q1 MATHEMATICS

Revista De La Real Academia De Ciencias Exactas Fisicas Y Naturales Serie A-Matematicas 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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Free Banach lattices under convexity conditions.

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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

Revista De La Real Academia De Ciencias Exactas Fisicas Y Naturales Serie A-Matematicas 数学-数学

CiteScore

4.70

自引率

17.20%

发文量

151

审稿时长

>12 weeks

期刊介绍： The journal publishes, in English language only, high-quality Research Articles covering Algebra; Applied Mathematics; Computational Sciences; Geometry and Topology; Mathematical Analysis; Statistics and Operations Research. Also featured are Survey Articles in every mathematical field.