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, 116 (15): 15.

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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

Additional Information:

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

Uncontrolled Keywords:

/dk/atira/pure/subjectarea/asjc/2600/2600

Subjects:

?? free banach latticep-convex banach latticeam-spacep-summing mapgeneral mathematics ??

Departments:

Faculty of Science and Technology > Mathematics and Statistics

ID Code:

160253

Deposited By:

ep_importer_pure

Deposited On:

05 Oct 2021 14:00

Refereed?:

Yes

Published?:

Published

Last Modified:

01 Dec 2024 00:37

URI:

https://eprints.lancs.ac.uk/id/eprint/160253