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arXiv · 2101.03510

Free Banach lattices under convexity conditions

Héctor Jardón-Sánchez·Niels Jakob Laustsen·Mitchell A. Taylor·Pedro Tradacete·Vladimir G. Troitsky
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Abstract

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 (\emph{Israel J.\ Math.}~2019). In the $p$-con\-vex 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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Héctor Jardón-Sánchez, Niels Jakob Laustsen, Mitchell A. Taylor, Pedro Tradacete, Vladimir G. Troitsky. 2021-01-10. Free Banach lattices under convexity conditions. https://arxiv.org/abs/2101.03510

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