Abstract
AbstractWe 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.
Funder
Agencia Estatal de Investigación
Ministerio de Ciencia, Innovación y Universidades
Consejo Superior de Investigaciones Científicas
Fundación Masaveu
Fundación La Caixa
Natural Sciences and Engineering Research Council of Canada
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Mathematics,Geometry and Topology,Algebra and Number Theory,Analysis
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