Free Banach lattices under convexity conditions

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

doi:10.1007/s13398-021-01155-8

Free Banach lattices under convexity conditions

Rev R Acad Cienc Exactas Fis Nat A Mat. 2022;116(1):15. doi: 10.1007/s13398-021-01155-8. Epub 2021 Oct 11.

Authors

Héctor Jardón-Sánchez¹, Niels Jakob Laustsen¹, Mitchell A Taylor², Pedro Tradacete³, Vladimir G Troitsky⁴

Affiliations

¹ Department of Mathematics and Statistics, Fylde College, Lancaster University, Lancaster, LA1 4YF UK.
² Department of Mathematics, University of California, Berkeley, CA 94720 USA.
³ Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM) Consejo Superior de Investigaciones Científicas, C/ Nicolás Cabrera, 13-15, Campus de Cantoblanco UAM, 28049 Madrid Spain.
⁴ Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1 Canada.

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.

Keywords: AM-space; Free Banach lattice; p-convex Banach lattice; p-summing map.