Free Banach lattices under convexity conditions

Jardon-Sanchez, Hector and Laustsen, Niels and Taylor, Mitchell A. and Tradacete, Pedro and Troitsky, Vladimir (2021) Free Banach lattices under convexity conditions. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas. (In Press)

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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 (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.

Item Type:
Journal Article
Journal or Publication Title:
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600
Subjects:
ID Code:
160253
Deposited By:
Deposited On:
05 Oct 2021 14:00
Refereed?:
Yes
Published?:
In Press
Last Modified:
05 Oct 2021 14:00