Lipschitz free p-spaces for 0 < p < 1
This paper initiates the study of the structure of a new class of p-Banach spaces, 0 <p < 1, namely the Lipschitz free p-spaces (alternatively called Arens—Eells p-spaces) Fp(M) over p-metric spaces. We systematically develop the theory and show that some results hold as in the case of...
| Autores: | , , , |
|---|---|
| Tipo de documento: | artigo |
| Estado: | Versión aceptada para publicación |
| Data de publicação: | 2020 |
| País: | España |
| Recursos: | Universidad Pública de Navarra |
| Repositório: | Academica-e. Repositorio Institucional de la Universidad Pública de Navarra |
| OAI Identifier: | oai:academica-e.unavarra.es:2454/39430 |
| Acesso em linha: | https://hdl.handle.net/2454/39430 |
| Access Level: | Acceso aberto |
| Palavra-chave: | p-Banach spaces Lipschitz free p-spaces |
| id |
ES_97440625f8efddc0eca01d0a72fc52b1 |
|---|---|
| oai_identifier_str |
oai:academica-e.unavarra.es:2454/39430 |
| network_acronym_str |
ES |
| network_name_str |
España |
| spelling |
Lipschitz free p-spaces for 0 < p < 1 Albiac Alesanco, Fernando José Ansorena, José L. Cúth, Marek Doucha, Michal p-Banach spaces Lipschitz free p-spaces This paper initiates the study of the structure of a new class of p-Banach spaces, 0 <p < 1, namely the Lipschitz free p-spaces (alternatively called Arens—Eells p-spaces) Fp(M) over p-metric spaces. We systematically develop the theory and show that some results hold as in the case of p = 1, while some new interesting phenomena appear in the case 0 <p < 1 which have no analogue in the classical setting. For the former, we, e.g., show that the Lipschitz free p-space over a separable ultrametric space is isomorphic to ℓp for all 0 <p ≤ 1. On the other hand, solving a problem by the first author and N. Kalton, there are metric spaces N⊂M such that the natural embedding from Fp(N) to Fp(M) is not an isometry. F. Albiac acknowledges the support of the Spanish Ministry for Economy and Competitivity Grants MTM2014-53009-P for Análisis Vectorial, Multilineal y Aplicaciones, and MTM2016-76808-P for Operators, lattices, and structure of Banach spaces as well as the Spanish Ministry for Science and Innovation under Grant PID2019-1077701GB-I00. J. L. Ansorena acknowledges the support of the Spanish Ministry for Economy and Competitivity Grant MTM2014-53009-P for Análisis Vectorial, Multilineal y Aplicaciones. M. Cúth has been supported by Charles University Research program No. UNCE/SCI/023 and by the Research grant GACR 17-04197Y. M. Doucha was supported by the GACR project 16-34860L and RVO: 67985840. Springer Hebrew University Magnes Press https://hdl.handle.net/2454/39430 |
| title |
Lipschitz free p-spaces for 0 < p < 1 |
| spellingShingle |
Lipschitz free p-spaces for 0 < p < 1 Albiac Alesanco, Fernando José p-Banach spaces Lipschitz free p-spaces |
| title_short |
Lipschitz free p-spaces for 0 < p < 1 |
| title_full |
Lipschitz free p-spaces for 0 < p < 1 |
| title_fullStr |
Lipschitz free p-spaces for 0 < p < 1 |
| title_full_unstemmed |
Lipschitz free p-spaces for 0 < p < 1 |
| title_sort |
Lipschitz free p-spaces for 0 < p < 1 |
| author |
Albiac Alesanco, Fernando José |
| author_facet |
Albiac Alesanco, Fernando José Ansorena, José L. Cúth, Marek Doucha, Michal |
| author_role |
author |
| author2 |
Ansorena, José L. Cúth, Marek Doucha, Michal |
| author2_role |
author author author |
| topic |
p-Banach spaces Lipschitz free p-spaces |
| topic_facet |
p-Banach spaces Lipschitz free p-spaces |
| description |
This paper initiates the study of the structure of a new class of p-Banach spaces, 0 <p < 1, namely the Lipschitz free p-spaces (alternatively called Arens—Eells p-spaces) Fp(M) over p-metric spaces. We systematically develop the theory and show that some results hold as in the case of p = 1, while some new interesting phenomena appear in the case 0 <p < 1 which have no analogue in the classical setting. For the former, we, e.g., show that the Lipschitz free p-space over a separable ultrametric space is isomorphic to ℓp for all 0 <p ≤ 1. On the other hand, solving a problem by the first author and N. Kalton, there are metric spaces N⊂M such that the natural embedding from Fp(N) to Fp(M) is not an isometry. |
| publishDate |
2020 |
| format |
article |
| status_str |
acceptedVersion |
| url |
https://hdl.handle.net/2454/39430 |
| eu_rights_str_mv |
openAccess |
| publisher |
Springer Hebrew University Magnes Press |
| institution |
Universidad Pública de Navarra |
| collection |
Academica-e. Repositorio Institucional de la Universidad Pública de Navarra |
| reponame_str |
Academica-e. Repositorio Institucional de la Universidad Pública de Navarra |
| instname_str |
Universidad Pública de Navarra |
| _version_ |
1878736900071620608 |
| publishDateSort |
2020 |
| author_browse |
Albiac Alesanco, Fernando José Ansorena, José L. Cúth, Marek Doucha, Michal |
| publisherStr |
Hebrew University Magnes Press Springer |
| score |
6,8972664 |