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  • FBLp_revised_sep2021_v2

    Rights statement: The final publication is available at Springer via https://doi.org/10.1007/s13398-021-01155-8

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Free Banach lattices under convexity conditions

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Article number15
<mark>Journal publication date</mark>11/10/2021
<mark>Journal</mark>Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas
Issue number15
Volume116
Number of pages25
Publication StatusPublished
<mark>Original language</mark>English

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.

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The final publication is available at Springer via https://doi.org/10.1007/s13398-021-01155-8