Free Banach lattices under convexity conditions

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 o...

Descripción completa

Detalles Bibliográficos
Autores principales: Jardón-Sánchez, Héctor, Laustsen, Niels Jakob, Taylor, Mitchell A., Tradacete, Pedro, Troitsky, Vladimir G.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2021
Materias:
Original Paper
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8550548/
https://www.ncbi.nlm.nih.gov/pubmed/34776812
http://dx.doi.org/10.1007/s13398-021-01155-8
_version_ 1784590978920742912
author Jardón-Sánchez, Héctor
Laustsen, Niels Jakob
Taylor, Mitchell A.
Tradacete, Pedro
Troitsky, Vladimir G.
author_facet Jardón-Sánchez, Héctor
Laustsen, Niels Jakob
Taylor, Mitchell A.
Tradacete, Pedro
Troitsky, Vladimir G.
author_sort Jardón-Sánchez, Héctor
collection PubMed
description 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.
format Online
Article
Text
id pubmed-8550548
institution National Center for Biotechnology Information
language English
publishDate 2021
publisher Springer International Publishing
record_format MEDLINE/PubMed
spelling pubmed-85505482021-11-10 Free Banach lattices under convexity conditions Jardón-Sánchez, Héctor Laustsen, Niels Jakob Taylor, Mitchell A. Tradacete, Pedro Troitsky, Vladimir G. Rev R Acad Cienc Exactas Fis Nat A Mat Original Paper 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. Springer International Publishing 2021-10-11 2022 /pmc/articles/PMC8550548/ /pubmed/34776812 http://dx.doi.org/10.1007/s13398-021-01155-8 Text en © The Author(s) 2021 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Original Paper
Jardón-Sánchez, Héctor
Laustsen, Niels Jakob
Taylor, Mitchell A.
Tradacete, Pedro
Troitsky, Vladimir G.
Free Banach lattices under convexity conditions
title Free Banach lattices under convexity conditions
title_full Free Banach lattices under convexity conditions
title_fullStr Free Banach lattices under convexity conditions
title_full_unstemmed Free Banach lattices under convexity conditions
title_short Free Banach lattices under convexity conditions
title_sort free banach lattices under convexity conditions
topic Original Paper
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8550548/
https://www.ncbi.nlm.nih.gov/pubmed/34776812
http://dx.doi.org/10.1007/s13398-021-01155-8
work_keys_str_mv AT jardonsanchezhector freebanachlatticesunderconvexityconditions
AT laustsennielsjakob freebanachlatticesunderconvexityconditions
AT taylormitchella freebanachlatticesunderconvexityconditions
AT tradacetepedro freebanachlatticesunderconvexityconditions
AT troitskyvladimirg freebanachlatticesunderconvexityconditions

Ejemplares similares