期刊
出版社
SPRINGER-VERLAG ITALIA SRL
DOI: 10.1007/s13398-021-01155-8
关键词
Free Banach lattice; p-convex Banach lattice; AM-space; p-summing map
资金
- CRUE-CSIC agreement
- Springer Nature
- Agencia Estatal de Investigacion (AEI) [PID2020-116398GB-I00, MTM2016-76808-P, MTM201675196-P]
- Fondo Europeo de Desarrollo Regional (FEDER) [PID2020-116398GB-I00, MTM2016-76808-P, MTM201675196-P]
- Spanish Ministry of Science and Innovation, through the Severo Ochoa Programme for Centres of Excellence in RD [CEX2019-000904-S]
- Consejo Superior de Investigaciones Cientificas (CSIC), through Ayuda extraordinaria a Centros de Excelencia Severo Ochoa [20205CEX001]
- Fundacion Maria Cristina Masaveu Peterson through its Scholarships for Academic Excellence
- Fundacion la Caixa through its Postgraduate Studies in Europe Fellowships
- Natural Sciences and Engineering Research Council of Canada
This article proves the existence of free objects in certain subcategories of Banach lattices and analyzes specific subcategories, leading to conclusions.
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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