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: | , , , |
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| 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 |
| Resumo: | 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. |
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